The Danza: Joseph Gatt's character was originally called GATT2000, although by the time of the film's release, the character's name was changed to Science Officer 0718.
Fake Nationality: The character of Khan is Indian, but he's played by the white British Benedict Cumberbatch.
Which makes sense, as if you recall in the original timeline The Enterprise's crew were able to identify Khan quite easily from historical documents. Section 31 giving him surgery so that he looks completely different is an entirely logical step to take in order to hide his identity.
Fan Nickname: "Star Trek XII: The Wrath of John" It turned out to be quite appropriate.
JJ Abrams and the film's writers said they didn't feel comfortable tackling an updated version of Khan. They lied. Likewise, Benedict Cumberbatch swore up and down that his character in the movie was original; and until his character was officially named John Harrison, the entire cast vehemently denied he was playing Khan whenever they were asked about it.
Leonard Nimoy said he had nothing to do with this film. He lied, as he got a cameo.
Historical In-Joke: The USS Vengeance is described as a Dreadnought-class starship, and a revolutionary new design. In Real Life, the commissioning of HMS Dreadnought, with her powerful steam turbine powerplant and all-big-gun weapons loadout led to a revolution in naval warfare, with all battleships henceforth described as being "Dreadnoughts" or "Pre-Dreadnoughts". Indeed, HMS Dreadnought is the Trope Namer for massive Game Breaker warships being called Dreadnoughts.
Interestingly, it has a second parallel with the original Dreadnought: It wasn't actually that impressive. The HMS Dreadnought only ever sunk one ship in wartime, and it was by ramming it. Likewise, despite the upgrades that went into the USS Vengeance, it is incapable of taking out a single older-model ship (The USS Enterprise).
Although in the case of the original Dreadnought, this was because there was only one major battleship battle during World War One, while Dreadnought was in port in the middle of some refits. Most of both nations' battleships were held back in reserve, the idea being not to risk such valuable assets until the enemy had committed his own.
The design of Earth's cities now has a very Mass Effect-like look and feel. From the vehicles, to the architecture, you'd half-expect to see a derelict Reaper near London. The Klingon ruins suggest a cross between Tuchanka and Ilos.
When Harrison takes out the Starfleet High Command early in the movie, it resembles the scene in The Godfather Part III.
Nibiru, the name of the planet in the opening scene, is the ancient Babylonian name for Jupiter (which has also been used in a couple of different pseudoscientific theories involving planetary catastrophes).
The room where the Starfleet captains confer and are eventually ambushed by Harrison looks very much like the archetypal war room seen in films like Dr. Strangelove and Fail-Safe.
Some fans were no doubt rolling their eyes when Abrams seems to setup a monster chase scene early in the film. The creature is instantly stunned and never seen again. Adding to the humour, it turned out that the monster was actually Kirk's ride, intended to help him escape from the horde of angry tribals pursuing him.