What An Idiot / The Big Bang Theory

Has a PhD in physics. Still thinks manually pushing a 4000 pound car in Park mode is possible.

Sheldon: (to Penny) We've already established that I'm found in the periodic table.
Penny: Well, it's a table right? I mean, why can't there be food on it?

— Sheldon and Penny playing (or arguing over) the "Guess what element am I" game

Despite being affiliated with CalTech and sophisticated fields of science, the main cast of The Big Bang Theory can be quite stupid because having knowledge of physics, astronomy, calculus and medicine doesn't always necessarily mean having common sense.

There are spoilers below. You've been warned.

Recurring

• Penny makes fairly low pay as a waitress at the Cheesecake Factory, especially when compared to Leonard, Sheldon, Howard, and Raj.
  You'd Expect: Penny to use her money only on basic necessities such as food, rent, and gas, and splurge as infrequently as possible, if at all.
  Instead: She wastes almost all of it on lavish berets and shoes.
  Results: Her poor spending habits have sunk her into trouble so badly that she's become desperate enough to borrow money from Sheldon in one episode and frequently mooches off of Leonard for restaurant carry-out meals and rent.

Season 1

• As explained in the pilot episode, Penny left her TV behind in Kurt's apartment room, and she's too afraid to challenge him to get it back because of his sheer strength.
  You'd Expect: Penny to get the police to retrieve it, or at least get someone strong to retrieve it.
  Instead: She sends Leonard and Sheldon, who are all brains and no muscle, to go fetch it. They return home empty-handed and pants-less.
• "The Grasshopper Experiment": Raj is frantic because his parents want him to meet up with Lalita, a childhood acquaintance, in the hopes that he will marry her. There are many problems with this: Raj can't talk to women, he remembers Lalita as little and fat, and he barely even knows her. Howard helps Raj arrange a date with her, and everyone finds out that Raj can talk to women if he's at least slightly tipsy. Penny decides a good plan of action is for her to bartend at the Cheesecake Factory so everyone can make sure Raj's date goes well.
  You'd Expect: Raj to only drink enough to get buzzed and to prepare ahead of time by preparing neutral conversation topics and doing research about what Lalita looks like and what her interests are. At the very least, he shouldn't be a drunk ass.
  Instead: He drinks so much that he is an awkward boor to Lalita, calling her "little Lalita" and loudly commenting on how she lost all her childhood baby fat. When Sheldon, who isn't interested in women at all at this point, compliments her and calls her a princess, Raj accuses Sheldon of trying to steal "his future wife".
  The Result: Lalita gives him a What the Hell, Hero? for being so boorish and asks Sheldon out to dinner because Sheldon is being much nicer than Raj and Lalita wants to salvage her bad night. Raj's parents angrily call him and demand an explanation. When Raj tries to blame Sheldon for stealing his date, Sheldon does apologize but also points out that Raj made a fool of himself by being "drunk and boring", so Sheldon didn't really have much to do with Raj messing up.

Season 2

• In "The Panty Piñata Polarization", after Penny touches one of Sheldon's onion rings without eating it, Sheldon and Penny start engaging in a war against each other. In an act of revenge for cutting off her Wi-fi, Penny uses up all the available washers in the laundry room to spite Sheldon.
  You'd Expect: Penny to watch her laundry carefully and make sure Sheldon doesn't take them away.
  Instead: She doesn't, which gives Sheldon the opportunity to hang her clothes on a telephone wire. It's only now, after ignoring/dismissing all of Leonard's warnings, does she realize that it's too late to convince Sheldon to forgive her.
• Sheldon comes up with an extension of Rock-Paper-Scissors called "Rock-Paper-Scissors-Lizard-Spock," played the same way except with five choices instead of three. However, every game ends with a hung decision because everyone always picks "Spock".
  You'd Expect: One of them to catch on and choose "paper" or "lizard", the two things that beat "Spock".
  Instead: They don't, because it's a sitcom and everyone wants to be Spock more than they want to win.
• In "The Cushion Saturation", the men play paintball and Sheldon brings a paintball gun back to the apartment leaving it on a table next to his preferred couch spot. Penny finds it and picks it up.
  You'd Expect: Leonard to tell her to put it down, as she clearly has no experience handling one.
  Instead: He encourages her to join them on their next game, and Penny foolishly opens fire at the cushion, ruining Sheldon's spot.
  You'd Then Expect: Penny to swap cushions since all three have been sat on routinely. That way, Sheldon wouldn't be able to tell the difference and Leonard can have it cleaned and washed at a shop. Alternatively, she could unzip the ruined cushion case and swap it with a clean cushion case so Sheldon's spot keeps the same cushion, just with a different case.
  Instead: Penny suggests to Leonard they lie to Sheldon that somebody broke in. When Leonard points out that nobody would break in just to shoot the couch with a paintball gun, she flips over Sheldon's cushion upside-down rather than swap it with another cushion, which causes Sheldon to notice that his spot is ruined.

Season 3

• In "The Vengeance Formulation", Sheldon gets payback at Kripke for unleashing helium onto the former's NPR interview by setting up tons of soapy foam (with help from Leonard and Raj) to drop onto him from his ceiling. However, Sheldon expected Kripke to be there alone in his own laboratory.
  You'd Expect: Leonard and Raj to convince Sheldon to add an abort button in case Kripke has guests over.
  Instead: Nobody thinks to do so, and they only tell him about the importance of such a button when they see that Kripke has the entire university board (including their boss Eric Gablehauser) in his lab showing them a presentation about something involving micro-controlled plasma.
  Results: Leonard and Sheldon's foamy concoction rains down on the entire university board.
  Bonus Idiot Points: Sheldon then reveals he did something even more stupid than forgetting the abort button: he deliberately sends a video that plays in front of the university board; this video not only reveals that he's the culprit but even implicates Leonard and Raj for their support of him.
• In "The Excelsior Acquisition", Sheldon receives a court summons for running a red light on the night he had to drive Penny to the hospital back in "The Adhesive Duck Deficiency" (while the ticket was sent to Penny since it was her car and license plate, she redirected it to Sheldon due to not wanting any more points on her driver's license). However, his court date happens to fall on the same day he and the boys are scheduled to have gelato with Stan Lee. When the boys refuse to accompany him, he drags Penny along to be his witness.
  You'd Expect: Sheldon to just pay the fine and be done with it so he doesn't miss out on his meetup with Stan Lee. Additionally, if he really insists on contesting the ticket, he could explain that he was driving Penny to the hospital and, in a fit of agony, she urged him to go when the light turned yellow, using the traffic cam's picture as evidence. While it probably wouldn't have dropped the fine, he'd at least have a valid reason for running the red light.
  Instead: He not only refuses to pay the fine (claiming that would mean "he's guilty"), but he also insults the traffic court judge to his face. This lands him in jail, puts points on a license he doesn't yet have, gives him a criminal record, and causes him to miss out on gelato with Stan Lee.
• In "The Wheaton Recurrence", Leonard tells Penny he loves her and a shocked Penny can only respond with "thank you". This creates tension between them, and they end up arguing during a bowling match against Wil Wheaton and Stuart after Penny leaves. Sheldon angrily demands a rematch to settle the score with Stuart and Wil's team.
  You'd Expect: Sheldon to reschedule the match for a later date and allow Leonard and Penny to try to resolve their issues first, as Penny is Sheldon's secret weapon due to her skills.
  Instead: Due to his self-centeredness, Sheldon forces Leonard and Penny to resolve their issues immediately.
  As A Result: Leonard and Penny do try to reconcile; however, the tension between them remains. In the next bowling match, Wil exploits this and convinces Penny to break up with Leonard right there and forfeit the match, which causes Sheldon's team to lose and have to dress up as female superheroes.

Season 4

• "The Love Car Displacement": Leonard gets angry when he finds out that a man whom Bernadette used to date is chauffeuring Penny a ride back to L.A. after a disastrous Science Conference. Not helping is the main cast (pars Sheldon) being unable to control their emotions and fighting amongst themselves. Due to these two things, Leonard gets a case of road rage and starts speeding, which Sheldon notices.
  You'd Expect: Sheldon and Amy to tell Leonard to slow down, because (obviously) their safety is at risk here. Additionally, if a police car starts following them, they would at least tell Leonard directly so they don't get mistaken for trying to avoid the police.
  Instead: They try to play a game of "I Spy" to make Leonard guess the police car pursuing Leonard for going 120 miles per hour. Amy doesn't even bother telling Leonard until the policeman has already signaled him to pull over!
• In "The Hot Troll Deviation", Sheldon and Raj are involved in an Escalating Prank War due to Raj sharing Sheldon's office (or, more accurately, Raj decides to put up a giant desk inside Sheldon's office just to anger the latter).
  You'd Expect: Sheldon to file a complaint about Raj to Human Resources and, if he does decide to get in a prank war, to not fill his office with flammable malodorants. If he does decide to do that for whatever reason, then he would at least try not to use close to 10,000 times the amount he needs to.
  Instead: He does this and declares chemical warfare on Raj because, of course, Sheldon believes Raj is too intellectually inferior to challenge him.
  You'd Then Expect: Raj to notify someone that Sheldon was messing around with dangerous gases in his office so they could be dealt with safely. And to at least stay the hell away from the room until it's detoxified.
  Instead: He doesn't tell anyone, and then lights a candle in the office, causing an explosion. A burnt and injured Raj is forced to leave Sheldon's office in defeat.
• In "The Roommate Transmogrification": Raj temporarily moves in with Sheldon so Priya and Leonard can live together. Penny visits the apartment to use the Wi-Fi and stays for a drink.
  You'd Expect: Penny to just have one drink and leave after she's done using the Wi-Fi.
  Instead: Due to Sheldon being his usual self, she drinks way too much and ends up waking up in bed with Raj the following morning. While this is bad enough, she ends up getting caught by Howard and Raj while leaving the apartment.
  As A Result: The group dynamic is almost destroyed and Leonard is left very hurt. While Raj reveals that he and Penny literally just fell asleep together, Penny still descends into alcoholism due to hurting Leonard's feelings, and the group only narrowly manages to stay together due to Sheldon's antics.

Season 5

• In "The Speckerman Recurrence": Leonard is contacted by Jimmy Speckerman, his former high school bully, who wants to work with him on a project. Jimmy is unaware that his actions hurt Leonard (thinking they were a "comedy duo") and after being told where to shove it by Leonard, Jimmy shows up to Sheldon and Leonard's apartment drunk and apologizes, with Leonard accepting and allowing him to stay the night and sleep it off. Once Jimmy sobers up, he's back to bullying Leonard and refuses to leave when Leonard tells him to get out.
  You'd Expect: Leonard or Sheldon to threaten to call the police and, if he still doesn't leave, make good on that threat.
  Instead: Leonard tries to physically force him out.
  As a Result: Due to Leonard's lack of any strength whatsoever, Jimmy doesn't budge, and the next shot shows Leonard and Sheldon running downstairs away from him.

Season 6

• In "The Parking Spot Escalation", as Sheldon and Howard fight over a parking spot in CalTech, their girlfriends Amy and Bernadette join the fight as well, siding with their respective boyfriends. When Amy parks her car in the spot, Bernadette decides to have it towed. Then, after having to shell out $300 to reclaim her vehicle, Amy starts demanding Bernadette to either compensate her or get money from Howard to do so.
  You'd Expect: Bernadette to outright refuse to pay her a penny and deny any involvement in it by claiming that a towing company did it of its own accord.
  Instead: Bernadette gloats, "I'm the one who had it towed!", making Amy try to attack Bern with a bag full of coins. Said bag strikes Penny instead, breaking her nose and sending her to the ER.
• In "The Santa Simulation", the guys are playing a Christmas-themed quest of Dungeons and Dragons that involves the rescue of Santa Claus. When they start their quest, their characters find a secret door, and Howard plans to set up an invasion strategy.
  You'd Expect: Raj to listen to Howard in order to pass safely.
  Instead: Raj is too obsessed with rescuing Santa and rushes in without listening to Howard's advice.
  Result: He hits a tripwire that triggers a cannon and kills off his character, sending him out of the game and forcing him to spend the night with the girls so he's not alone.
• In "The Bakersfield Expedition", the men are in Star Trek: The Next Generation costumes and are taking pictures at a rock in the desert next to a freeway.
  You'd Expect: Leonard to take the keys out of his car and lock the doors.
  Instead: He leaves his keys in the ignition lock and doesn't bother locking the doors. This results in a car thief stealing it, forcing the men to cross the desert without any food or water while in costumes and heavy cosmetic make-up.

Season 9

• In "The Convergence Convergence", as the date is closing in on Penny and Leonard's upcoming wedding, the group is supposed to go to a restaurant. Howard, Bernadette, and Raj are in one car, while Leonard, Penny, and Leonard's mother Beverly are following them in another car.
  You'd Expect: Penny to let either Howard, Bernadette, or Raj know that they're following their car.
  Instead: She decides to "tell" them by having Leonard go faster and flash their headlights - which scares Howard into speeding away from them. She doesn't even try calling any of them until she finally arrives at the restaurant.
• On the flip side, Howard, Bernadette, and Raj are extremely paranoid that the government is coming after them due to an incident with a gyroscope and mistake Leonard's car for a car belonging to government agents.
  You'd Expect: Howard, Bern, and/or Raj to look at the license plate, make, and model of the car to see if it's something that a government agent would, in fact, drive. Additionally, Raj should try to see who the driver of the car behind them is, just to see if it's someone that they know isn't a government agent.
  Instead: Being alerted by Leonard flashing his lights, Bern orders Howard to speed away... and they get pulled over by a police officer, causing them to have to do a sobriety test and pay a $500 traffic fine.

Season 11

• In "The Retraction Reaction", Leonard is being interviewed by Ira Flatow (though we aren't informed if he was doing this of his own accord), even though Leonard can't name any recent achievements or breakthroughs in physics.
  You'd Expect: Leonard to prepare for the interview by either consulting Sheldon or his boss on what to say about physics because he can't think of a way to laud the current direction of research and progress done. If he doesn't want to do that, he should at least be somewhat optimistic during the interview.
  Instead: He tells Ira that he worries physics is a dead-end and even says that he wonders if donors should've reconsidered giving so much money to physics in the first place.
  Result: He is threatened with termination by his boss if he does not retract his statements, and Sheldon starts to lose hope in his career as well because of Leonard's statements.
• In "The BitCoin Entanglement", Sheldon gets revenge on Leonard, Howard, and Raj for mining bitcoins without him by transferring them off Leonard's laptop and onto another electronic device.
  You'd expect: Sheldon to transfer it to one of his own electronics so he can keep the bitcoins safe while still getting his revenge.
  Instead: He transfers it to Leonard's Batman keychain flash drive, which means he can't ensure the bit coins' security. Additionally, since it's Leonard's flash drive, the latter could easily notice the bitcoins on his flash drive and transfer them back to his computer (though how Leonard never noticed this between the time Sheldon transferred the bitcoins to the day they checked it is a completely different question).
  As a result: Leonard ends up losing the flash drive, and he reveals that he lost it years ago. The ending shows that Stuart found it in his comic book store 4 years prior and decided to erase and resell it for a mere $10, rendering all of their bitcoin mining efforts worthless.
• "The Sibling Realignment": In this episode, it's revealed that Sheldon has had a contentious relationship with his big brother Georgie, believing him to be an aloof bully. Georgie revealed that he didn't resent Sheldon for being the delicate child and baby of the family; his goal was actually to protect him from other mean kids. He only resented Sheldon because he didn't realize how much Georgie sacrificed for his family after their father died. Sheldon was in college when their mother had a breakdown, and Georgie dropped out of his program to help out because Missy was just a kid. He then says that they didn't tell Sheldon because he didn't want to burden his little brother.
  You'd Expect: That after Sheldon has grown up and gotten a degree and his own apartment, Georgie would tell Sheldon the truth, or at least invite him to talk it out. If Sheldon refuses, then Georgie has confirmation that his little brother is an oblivious Insufferable Genius. If Sheldon accepts, then they can talk things out and reform their bond. Holding that much resentment isn't healthy for either of them.
  Instead: Once their mother is stable and Missy has moved out, Georgie puts all of his energy into building a successful business in automotive repair, and never tried to reach out to Sheldon while the latter built a life on the West Coast studying physics.
  The Result: When he finally tells Sheldon the truth about what happened when their father died, after their mother forces Sheldon to invite Georgie to the former's wedding, they both realize they were being jerks. Sheldon apologizes to Georgie for not noticing how hard he worked to keep the family afloat, saying that he knows he can not notice what's in front of him. Georgie also acknowledges that he should have told Sheldon in the first place, treating him like an adult rather than as his kid brother, and forgives "Shellie", as he affectionately calls him.

Season 12

• In "The Laureate Accumulation", The university holds an event for Sheldon's and Amy's super-asymmetry discovery which is threatened by Drs. Campbell and Pemberton. Sheldon's and Amy's attempt to charm the Nobel Prize committee to keep up with the competition created by Pemberton's and Campbell's press tour and they have arrived at Sheldon's invitation so they can be exposed as frauds when questioned over their discovery .
  You'd Expect: Amy to follow Sheldon's plan and remain civil and curt with Campbell and Pemberton. The latter two have flunked their way into proving super-asymmetry and can easily be exposed as frauds with a few questions.
  Instead: Amy ends up having a meltdown and gives an absolutely blistering suck speech to Drs. Campbell and Pemberton for taking the credit for super-asymmetry.
  Result: Amy and Sheldon are forced to do damage control by the university in order to not lose their chances at winning a Nobel, which includes having to apologize to Pembleton and Campbell.