Doctor Nicholas Rush: Grieving widower who presents a facade of Insufferable Genius because he feels he needs to suffer, and is consumed with his genius and research so much that he can no longer comprehend social behavior? Or arrogant asshat who with one act of arrogance marooned over eighty people on the other side of the universe with a barely functioning ship facing constant danger?
Wray: Obstructive bureaucrat with a hidden agenda or concerned administrator trying to keep everyone out of the way of the politicking of the heads of the military and the heads of the scientists?
The Nakai. Considering how obsessed they are with capturing Destiny, it's possible that their extreme malice towards humans is because they see the crew as "stealing" the vessel away from them. Since they did not know of it being constructed by the Ancients (or its true mission), after finding out the former information from Chloe and Rush via their mind-probe, they may see their human's claim of inheritance as less valid than their long-standing claim of salvage.
In "Gauntlet", was Eli's claim that he could fix the pod genuine or was he willingly choosing to sacrifice himself to save all of his friends? Alternately, given that he repeatedly reassures everyone that he will be on the other side, was he planning on using the Control Chair to upload himself into Destiny and simply psyching himself to let his physical body die in the process?
The closing theme is a haunting, athmospheric piece that truly shows the situation aboard the Destiny is fucked. From what it seems, the theme was also supposed to be the intro (this video neatly visualises What Could Have Been if it was used for an intro as well) before the Syfy executives ordered a change to the Cold Opening "title card and short motif" intro in the finalised show.
The funny and touching use of 'The Worst Day Since Yesterday'.
Broken Base: From your "more realistic" camps to your "soap opera in space" camps, this series has a divide wider than the Grand Canyon. Even among the people who like the series, there is a gap between Young supporters and Rush supporters; this is probably deliberate, however.
Crossover Ship: "Rushbelle," the pairing of Nicholas Rush with Belle from Once Upon a Time, is popular in the fandom (given that Belle is the love interest of Robert Carlyle's OUAT character Rumplestiltskin).
Engaging Chevrons: Used when the Destiny is first dialed, but mostly ignored after that. There's also this: "Chevron Nine... Chevron Nine... Chevron Nine..." Makes a return in "Earth" when they attempt to dial, you guessed it, Earth, but one might excuse this as going slow because they were afraid they'd blow the ship up.
Vanessa James role was mostly Fanservice, if occasionally self-aware Fanservice. Her fan nicknames tended towards things like "2nd Lt. Tits McGee".
GateFail2009 (or just GateFail) to refer to the whole series, resulting from die-hard fans upset about the lack of previously known characters, consistent mythology within the Stargate franchise, or the Soap OperaIN SPACE!! nature of the series as opposed to the sci-fi adventure format of SG1 and SGA. As well as feminists complaining about...feministy stuff. And, lest we forget, Battlegate Voyager 90210.
"Smurfs" is a commonly used name for the blue, catfish-like aliens hunting the Destiny
Sergeant Greer's early apparent temper problems caused him to be referred to as Furious George.
Fanon Discontinuity: Tainted by the synopsis and casting calls, many fans preemptively disowned the show as non-canon before it even aired.
Fan-Preferred Couple: While Nicholas Rush holds a candle for his dead wife and Everett Young has his affair with TJ, most fanfiction instead pairs them with each other, due to their intense rivalry and the real-life friendship between their actors. In fact, Rush has been shipped with almost every other character. In particular, Eli and Chloe are mostly shipped with Rush over their canon love interests Scott and Ginn.
Gateway Series: Some of the show's most vocal proponents are people who never watched the first two Stargate series or weren't big fans of them. IGN's Ramsley Isler is one such individual, as is Tycho of Penny Arcade. Some of them, true to this trope, have even decided to start watching the old series just to see what all the fuss was/is about.
Genius Bonus: Anyone who ever learned (or at least glanced) at the Ancient language symbology on the Stargate SG-1 webpage would know that the symbols on the ship's gate are simply numbers, which would make sense for a ship that goes from galaxy to galaxy and would have no common astronomical reference points.
Growing the Beard: Season 2 made tremendous strides forward with the show's formula, trading off much of the criticized Wangst for more action and exploration. "The Greater Good" is commonly seen as a turning point, resolving the ongoing Young/Rush conflict and setting off the series' Myth Arc. And then Syfy canceled it.
Inferred Holocaust: The fate of the alternate crew's descendants from Novus, presuming they weren't all evacuated on their ships. At least one of their colonies had already fallen victim to the Berserker Drones and since they demonstrate advanced reasoning abilities, enough to cut off Destiny from every gate and star in their flightpath, it's very likely that the Novus Generation Ship will eventually come across them.
Coupled with the fact that the Nakai have reached the galaxy as well in their hunt for Destiny and may stick around while they try to figure how they lost its trail post-"Gauntlet". And then there's the sentient fungus from "Cloverdale" that possibly may have spread to other worlds. Chances are good that even if the people of Novus do reach their new settlement and meet up with the colonists that the crew rescued, they're pretty much screwed in the long run.
Macekre: The German dub, apart from having atrocious voice acting that did not fit the characters at all, also contained several translation errors, some of whom completely change important plot elements. For example, in the German dub, it is literally said that Destiny is flying "with light speed connected through hyperspace", while actually the exact and complete opposite is true.
Mis-blamed: A lot of fans from SG-1 and Atlantis blamed it for the cancellation of Atlantis. According to co-creator Brad Wright, Universe had been shelved for more than a year because they didn't want to try and run two series simultaneously again, the way they did for awhile with SG-1 and Atlantis, only getting greenlit because Atlantis was on the way out. On the other hand Joseph Mallozzi has said that they were expecting to be renewed for a sixth season of Atlantis and that both shows would have run at the same time.
Moral Event Horizon: Pick one for Simeon: killing Ginn AND Dr. Perry with one action, rampaging through the ship killing and wounding multiple security guards, taking Dr. Park hostage and attaching a bomb to her back, and finally taunting Rush about Perry's death, claiming he (Simeon) left Rush alive so Rush could suffer remorse and guilt Any one of those could qualify, but all of them put together put Simeon far beyond the MEH.
Not to mention it makes things a heck of a lot worse for the other LA members who are genuinely trying to cooperate and play nice.
Older Than They Think: The backlash that erupted over a character's faith being treated positively. Those involved should take a closer look at Stargate SG-1 season three, where "Demons" has a supporting character from the medieval planet willing to stand up to a Goa'uld-infested Unas thanks to his faith.
Paranoia Fuel: The communication stones. They allow their user to take control of another body over any distance. Of course, it only works if that body has a communication stone of its own, but the potential for abuse is there if the user decides to do things with their body that the other person didn't expect or consent to. Especially if they get hijacked by aliens.
Of course, when SGC starts using it to take over uncooperative allied politicians... well, it's not paranoia then!
The Scrappy: Chloe. The writers recognised her status as The Load and addressed late in Series 1, finally getting her off her ass and contributing something to the team. Series 2 goes at great lengths to make sure she's Rescued from the Scrappy Heap.
Squick: The unfortunate way that Red Shirt Gorman gets sliced by the cloud of alien bugs in "Water". Followed two episodes later by large worm/squid-like creatures that burrow through your skin to eat your yummy insides then eat their way back out. Brrrr.
Strawman Has a Point: Telford's rant makes some sense, at least on the surface, if we consider him a Straw Traitor. It falls apart when you actually take a good look at the people he's arguing on behalf of.
One could argue that Rush was entirely right that Young isn't fit for command. Yes, framing the man for murder was a dick move of epic proportions, but Rush is still their most valuable asset in terms of keeping Destiny functioning and the crew alive. Beating the shit out of him and leaving him for dead was serious Disproportionate Retribution and incredibly irresponsible.
Rush, Wray and half of the civilian crew enacting a coup in "Divided", claiming that they are essentially under a military dictatorship and subject to martial law. When we see that the marines (even Greer) fully prepared to shoot the civilians trapped on the wrong side of the line just for talking back to them, it's hard to deny that Rush and Wray are right. Especially considering that Wray and (begrudgingly) Rush are trying to prevent deaths throughout the entire ordeal.
Franklin, Curtis and Palmer do make a very good case to Eli in Air, Part 3 for wanting to flee the desert planet for one of the unmapped worlds as the Ancients almost certainly did have a better way to search for the materials they need than wandering the desert aimlessly, they absolutely would have been able to stop the ship for more than twelve hours to search for it, and on a ship this old and broken, there actually was no guarantee that Destiny was even giving them the correct information.
Tainted by the Preview: Several fans on the Syfy forum were put off by the casting calls for the main cast, with things like Chloe's describing her as a "party girl" and Lt Scott's calling him "every teenage girl's fantasy" giving the impression that this series would be more shallow and teen-oriented, inviting comparisons to the 'teen SG-1' parody sequence from the episode "200".
They Changed It, Now It Sucks!: There was already a great deal of complaining that the show would be vastly inferior to previous incarnations of Stargate before airing. Then it aired, and the complaints kept coming.
This is also a potential opinion of the series as a whole. An Ancient ship with mysterious retro-advanced technology, exploring unknown parts of the galaxy with more truly alien creatures and forms of life than the original two series ever had... and the characters are the bunch of the whiniest, least curious, least suitable twerps you could ask for.
During "Seizure", at no point does anyone discuss Langara having been under Ori occupation, nor what happened to Jonas Quinn.
Too Bleak, Stopped Caring: It's hard to care about the characters in a show whose first episodes exude an aura of hopelessness and mostly contain directionless conflict among the team. This is only compounded because its predecessors were thematically about adventure and prevailing over other adversaries.
Ugly Cute: The aliens in "Awakening" may be bug people, but you can't deny that first one looks cute while it's curled up in a ball and hugging its legs.
Not to mention the adorable sounds it makes, reminiscent of baby raccoons.
The aliens chasing Destiny actually are somewhat cute. It's just unfortunate they're a bunch of colossaldicks.
The Un-Twist: Telford is a mole. So unsurprising it's surprising.
Visual Effects of Awesome: The ship is a thing of beauty, as is its so-far-exclusive hyperspace window effect. Also, the Stargate surface is so pretty it's hypnotic (and it ain't just down to advances in special effects tech — Stargate: Continuum's isn't as pretty.)
As far as the gate is concerned, this is probably due to the much more varied environments and angles we see the gate in compared to previous shows. To initially save money, the gate effect was filmed (for the original SG-1 show) from a number of angles and these stock pieces used over and over.
The Woobie: Everett, Future!Rush in "Twin Destinies", Eli, Chloe, Vanessa
of "Air, Part 3" is a frequently cited example.