Captain's Log: A quick and easy way to set the stage for an episode. Mental masturbation aside, there really isn't any rhyme or reason to the decimal digits; the general rule is that 1,000 stardate units are equal to one year, the normal timespan between TV seasons. Starfleet is still using the Roman calendar at the time of ENT.
Actor Allusion: As Spock Prime, Leonard Nimoy introduces himself saying "I am Spock", which was the title of his second autobiography (so titled to rebut the notion that I Am Not Spock created, which was how he supposedly hated both Star Trek and the Spock character).
Dawson Casting: Most of the cast is semi-plausibly close to the ages of recent Starfleet Academy graduates. However, John Cho is a 37-year-old playing the 21-year-old Sulu. Karl Urban is also 37, though he's closer to his character's official age of 30. And Zoe Saldana (Uhura) is 31.
Deliberate Flaw Retcon: Used on many occasions by the writers to justify inconsistencies with the franchise, for example about the Vulcan sky suddenly being blue (it's a season thing now) or the Federation spaceships being way too advanced for their time period (the Starfleet engineers made use of scans from Nero's 24th century mining ship).
Englishman Simon Pegg as Scotty, who is, well, Scottish (though James Doohan was Canadian, so this might be closer).
Dominican/Puerto Rican-American Zoe Saldana as African-born Uhura (though Nichelle Nichols is straight-up African American so this isn't really any different)
Interestingly, the most blatant example from the original series is averted. Leningrad-born but American-raised Anton Yelchin plays Chekov, originally played by American Walter Koenig with a fairly ridiculous Russian accent. Yelchin kept the accent, purportedly as an Homage, but just because he's a Russian/English bilingual native speaker doesn't necessarily mean he can realistically speak English with a Russian accent.
Lying Creator: Paramount's pitch was that it was bringing in new writers specifically for new ideas. Then the first trailer showed us...Captain Kirk. While people ultimately still liked the movie, retuning to the original characters and timeline wasn't what anyone was thinking when they heard "new".
Playing Against Type: The case could be made for several members of the cast, but the biggest examples are probably Karl Urban as the cantankerous McCoy instead of a badass warrior, JohnCho as a grade-A asskicker instead of his frequent comedic fare, and Eric Bana (and not Zachary Quinto) as the Big Bad.
Production Posse: J.J. Abrams brought in usual collaborators such as producer Damon Lindelof, composer Michael Giacchino,editor Mary Jo Markey, actors Bruce Greenwood and Greg Grunberg, and most of the crew of Mission: Impossible III.
Promoted Fanboy: Director J.J. Abrams actually downplayed his enjoyment of modern Trek to emphasize his love of the original series. Screenwriter Roberto Orci is an admitted fanboy as well. And Simon Pegg, who holds the now-famous irony of his statement on Spaced that odd-numbered Trek films suck.
Tyler Perry, of Madea fame, was a Trek fan, they got him a guest appearance as the Dean of Starfleet Academy. Randy Pausch, who listed being captain of the Enterprise as one of his dreams in "The Last Lecture" appears as a bridge member of the Kelvin. He walks past the captain's chair, says, "Captain, we have visual", and is not seen again.
Most cast members agree that Karl Urban is the biggest Trek geek in the cast.
Real-Life Relative/Casting Gag: Spock mentions that Vulcan and Romulans share common ancestry. One of the Romulans shown when Kirk and Spock beam into the Narada is actually Zachary Quinto's brother Joe.
Shrug of God: J. J. Abrams really doesn't have an answer as to whether the policeman who pursues young Kirk during his joyride is a robot or not.