3rd Rock from the Sun: The Solomons are all advanced aliens who could make fools out of even the smartest human beings, yet, because they have never dealt with emotions before, they come off as utterly crazy and weird to everyone around them. Dick, in particular, is a pompous manchild who can't even teach a young girl to play hopscotch without turning it into an argument.
Adam Ruins Everything: The titular Adam is an expert in just about every subject matter there is but is absolutely terrible at predicting how people will react to things. For instance, in "Adam Ruins Security", he needs to have it pointed out to him that going on live TV and giving serial killers advice on how to get around common security systems might have unintended negative consequences.
The Adventures of Superman: Recurring Character Professor Pepperwinkle. Example: he brings his latest invention to show Perry White. It's an untested time machine. Perry doesn't have time to look at it because he's busy with an important story involving a gangster who is about to turn himself in to the authorities, and who is in his office at the time, so the Professor turns his time machine on and sends them all (himself, the gangster, Perry, Lois, Jimmy, and Clark) to prehistoric times. Success!... Then he realizes that he didn't bring enough fuel to make a return trip.
Angel: Winifred "Fred" Burkle may qualify. She's a skittish, timid, socially awkward girl, exacerbated by her imprisonment in another dimension where she was viewed as little more than cattle for several years, to the extent she verges on Cloudcuckoolander (at least in earlier seasons). She also happens to be a quantum physicist of near-genius intellect.
Bar Rescue: In one episode, Jon Taffer goes to save a bar called Paladino's, which has two owners, John and Jonathan, who are both scientists by day, but seem to have trouble running the bar. This comes to a head during the stress test when they can't figure out if they got an order of pizza right.
Jon: John and Jonathan are book brilliant, but they're common sense ignorant. They can't get a slice of pizza to a table without a ten-minute discussion. Jonathan: Jon Taffer called us morons, and he's absolutely right.
Sheldon Cooper may be a brilliant theoretical physicist, but he is insufferably arrogant, eternally confounded by social conventions, and almost completely ignorant of pop culture outside the sci-fi genre. He is an obsessive Rules Lawyer, writing out Roommate Agreements and even Couple Agreements. He even keeps a timetable for his bowel movements.
Raj is a gifted Astrophysicist, whose work is featured in scientific magazines, yet has a Sickening Sweethearts relationship with his dog and in early seasons was incapable to talking to women unless he had alcohol inside him.
Amy is a neurobiologist, again, excellent at what she does and again, hilariously inept at socializing. In spite of speaking a very deadpan tone of voice, she gets super excited when the other girls include her in their activities. Very rarely does a woman in her late twenties get that excited about being invited to a slumber party.
This was Bernadette's original characterization in Season 3 and early Season 4. She's introduced as a microbiologist with an interest in physics as well (every bit Howard's intellectual equal) but also rather ditzy, seemingly oblivious, and unable to understand Howard's jokes. However the ditzy aspect of her personality was dropped, probably to differentiate her more from Penny, and was replaced by her aggressive nature and Tsundere traits.
Experimental physicist Dr. Leonard Hofstadter, has the least outlandish quirks of the initial group and has a Ph.D. from Princeton. However, his unloving upbringing has left him extremely needy for validation and affection, to the extent that the first time he and his Penny slept together he wrote her a 10-PAGE LONG "Thank You" letter.. His attempts to look cool are hilariously inept (including the backwards baseball cap) and he once used the equipment from government-funded laser experiment to build his own Bat Signal.
Blackadder: Lord Edmund Blackadder from the second season. A transitional Blackadder, having gained a lot of cunning and suave that would grow with each of his predecessors, but still having some blithering, pitiful shades of the previous Edmund.
Bones: Bones is intelligent for solving crimes and yet clumsy with social stuff... Because her understanding of human behavior is more intellectual than intuitive, she forms conclusions that make perfect sense in theory but are flawed in practice because humans themselves are flawed. It was heartbreaking when she told Booth she was going to adopt a dog that had been trained as a killer, only for Booth to tell her that the dog had been put down because her protestations that the dog shouldn't have been blamed were right.
This is Hank's opinion of "Heisenberg" when he views security footage of Heisenberg breaking into a chemical warehouse with homemade thermite... and then struggling to carry a barrel out to his getaway car.
Hank: Look at this — they're smart enough to use thermite to cut through the lock, but they didn't think to bring a handcart? Try rolling it, morons! It's a barrel! It rolls!
This ends up being true of Hank's assessment of Walt in Ozymandias telling him, "You're the smartest guy I ever met and yet you're too stupid to see, he made up his mind 10 minutes ago.
Criminal Minds: Reid often qualifies, although he's working on it, in his odd Reid way. He's very good at numbers, statistics and abnormal psychology of all kinds, but no good at all, most of the time, at things like the unspoken rules of conversation and tact.
Doctor Who: The Doctor. He's eccentric, more than slightly manic, rarely compliments anyone's intelligence without mentioning his own, and has the ability to, without fail, sniff out and leap headfirst into any danger that his companion hasn't already stumbled into. Oh, and he's also a ridiculously competent Genius who's saved the Earth countless times, but that's nothing you'd be able to tell at first glance. Especially not if you're glancing at his sixth incarnation. Or the Fourth. Or the Tenth. Or... any version of him, for that matter. But Six is especially bonkers. Eight has a definite case of Attention Deficit... Ooh, Shiny! going on, too (as does Eleven, for that matter), both in the movie and the Eighth Doctor Adventures novels:
Eighth Doctor: A meteor storm. The sky above us was dancing with lights. Purple, green, brilliant yellow. YES! Grace: What? Eighth Doctor: These shoes! They fit perfectly!
Family Matters: Steve Urkel is a scientific genius, building all sorts of inventions. However, he is very clumsy and lacking in social skills.
Family Ties: Alex P. Keaton. He's a hypercompetitive straight-A student and math genius who was doing his parents' taxes when he was five years old and advised his parents on mortgage rates when they bought their house. Yet in everyday activities, he often proves completely incapable. His little sister frequently beats him in sports, he fails at things like building kites, cooking or fixing cars even with extensive directions.
The Fresh Prince of Bel-Air: Carlton Banks may be a book-smart and highly intelligent first-class high school (later college) preppy, but he is especially naïve and immature, especially in later seasons, and on multiple occasions seems to be Oblivious to Love. These areas are his cousin Will's expertise and he is often forced to (whether he wants to or not) bail Carlton out of social situations where such happens.
Gilligan's Island: Mrs. Howell is this crossed with Rich in Dollars, Poor in Sense. She's quite intelligent in a number of ways, is apparently second to the Professor in terms of formal education (though her expertise lies more in art and culture), and is a source of motherly wisdom, but lacks basic sense and can act pretty scatterbrained at times.
Glee: Kurt Hummel is very intelligent and a fluent French speaker, but prone to moments of ditziness, such as his belief boxes have four sides or his plan to feed the doves at Burt and Carole's wedding glitter.
Good Omens (2019): Aziraphale is clever enough to track down the Antichrist by deciphering the words of a notoriously eccentric prophetess, and takes on the assembled armies of Heaven and Hell with strategic Rules Lawyering via Exact Words. Foolish enough to visit Paris during the Reign of Terror while dressed in obviously expensive (and presumably aristocratic) high fashion because he missed French food. Crowley best sums it up with his exasperated shout of "You're so clever! How can someone as clever as you be so stupid?!" during his unsuccessful attempt to convince Aziraphale that his plan to get Heaven to call off the Apocalypse isn't going to work.
The Good Place: Chidi Anagonye is an expert in moral philosophy, but whenever he tries to actually apply his knowledge, he fails miserably and becomes incapable of making even the simplest decisions.
The IT Crowd: Moss is an extremely book smart technological genius, with No Social Skills and a rather absurd lack of common sense. When a fire broke out in his office, for instance, his reaction was to send a carefully worded e-mail to the fire department, then sit there and wait for them to respond.
Kamen Rider Double: Philip has access to all the knowledge of the earth and is quite smart in his own right, able to figure out many things that Shoutarou can't. However, due to Laser-Guided Amnesia and being trapped in a factory placidly taking orders for eleven years, he doesn't know things that most people consider rudimentary. When he happens upon a subject that he finds interesting (a place, a food, a type of dance...) he will obsessively look up everything he can about it, oftentimes dressing up in zany outfits or trying nearly-suicidal activities just because he can. Also, especially towards the beginning of the series, he has No Social Skills.
Leonardo: Leo is possibly the smartest person in the world, but is incredibly easy to manipulate due to automatically believing in people, much to the despair of his Street Smart friends.
Lois & Clark: Prof. Hamilton has discovered a way to clone dead people with all their old memories and personalities intact, as well as a way to alter personalities... so he brings back Al Capone, John Dillinger, and Bonnie and Clyde. Naturally, they all escape and wreak havoc across Metropolis. Lois even calls him out on it.
Lois: Hollywood's created a dozen versions of Frankenstein and you still didn't get the point.
Malcolm in the Middle: Malcom may have an IQ of 165, but he has the judgement of a drunk squirrel. To name a few showcases: he tanked his grades and got caught trying to drink underage just to impress a rather unintelligent girl, tried to crash his mother's car into his father's car to get sent to military school after he had been embarrassed the previous day, crashed his go-kart into Reese's for revenge for stealing his birthday money causing them to get both hospitalized and grounded with Dewey getting Malcolm's only birthday present, tried to dispose of a loaded gun rather than calling the cops, and held a pair of open scissors near his face right as Reese popped a balloon.
Adrian Monk is normally unable to function in society due to his severe obsessive-compulsive disorder and fear of just about everything. However, he's rather gifted academically, and once he sets foot in a crime scene, he can almost instantly solve the crime with the smallest or most overlooked pieces of evidence.
Monk's brother exhibits similar qualities: He has an extreme case of agoraphobia that prevents him from (nearly) ever leaving his house (as well as a related phobia that prevents him from entering the study of their father), but is evidently a highly skilled writer of technical manuals.
Sherlock: Sherlock. Justified as Sherlock only keeps important information in his "hard drive", which does not include tact, common sense, or the idea of heliocentrism. John pretty much calls Sherlock this in one episode:
John: You know, for a genius, you can be remarkably thick.
Richard Hendricks is an extremely talented programmer who has the ability to redesign an entire platform literally overnight. He also lacks basic common sense and has very poor decision-making skills.
Jared Dunn is a highly skilled business manager, who speaks with a high vocabulary, and is essential in keeping Pied Piper work productively and professionally. But he is helplessly clumsy and is quite inept when it comes to casual human conversation. His Extreme Doormat nature, out of nowhere references to pop-culture and utterly bizzare recollections of his Dark and Troubled Past often make him a complete social alien.
Stargate SG-1: Daniel Jackson is like this in the early seasons. One notable example is in the episode "1969", when the team goes back in time to the titular year and are captured by US military. A soldier asks them (in Russian) if they are Soviet spies, and Daniel immediately replies nyet ("no" in Russian).
Star Trek: The Next Generation: Commander Data represents the pinnacle achievement of robotics and is very likely the most intelligent officer in all of Starfleet. He is also routinely stymied by basic human interaction and language.
Chief O'Brien: ...We'll be burning the midnight oil on this one. Data:That would be inadvisable... If you ignite a petroleum product on this ship at zero-hundred hours, you will activate the fire suppression system, which would seal off this entire compartment. O'Brien: That was just an expression. Data: Expression of what? [later] Data: It appears we will be required to ignite the midnight petroleum, sir.
Star Trek: Voyager: Ensign Harry Kim is a brilliant scientist and engineer, but also hopelessly inept when it comes to relationships to the point that he can't even get laid in his own holodeck simulations, and no con is so obvious that he won't fall for it hook, line, and sinker.
Wizards of Waverly Place: Justin Russo plays this trope pretty straight. He excels at academics but tends to have no common sense to the point that he seems to have the Idiot Ball glued to his hands.
