Also spoiler alerts and such. Don't normally do them but whatever you're warned.
Anywho, if you're a Trek fan you might have missed a lot of what this movie did to reference the original series. A good little fun fact is Captain Pike being in the movie. You may not know this, but Captain Pike was the original captain of the Enterprise in the original pilot episode of the series. Kirk didn't exist in the pilot and there were numerous things that greatly contrast with what Star Trek ended up being, but there usage of Pike as the first captain of the Enterprise in the film roots all the way back to this pilot episode. While later changes to the story would include another captain predating Pike, this only appeared in the animated series. It's also noteworthy that Pike ended up getting strongly injured in the original series similar to the 2009 film, but with more severity including full body paralysis. Pike also happened to be captured when heading into a trap due to a distress signal.
When Kirk, Sulu, and that other guy left the ship to destroy the mining drill (or laser thing which happened to jam communications) the extra guy (considering he didn't have a main character name...) happened to be wearing red. As anyone who watched the original series might know, a non-main character who leaves the ship dressed in red typically don't end up surviving the trip. Another reference in this scene is Sulu saying that he has combat training in fencing. This references an episode of the original series where crewmen start acting fairly crazy (I forgot why and don't feel like looking it up) and Sulu's part was running around with a fencing sword and challenging people to duels.
The Klingon war never takes place in the universe based on this movie. In the scene where Kirk is hiding under the green girl's bed, Uhura reveals that the entire Klingon fleet was destroyed. This completely erases many possible events from taking place in the Star Trek universe. The fleet was destroyed by Nero's ship which was first revealed and described as "a lightning cloud in space". This is interesting since the first Star Trek film started with 3 Klingon vessels being destroyed by a similar anomaly. Even more interesting is both "lightning clouds" ended up being devices centered around time, the first being a relic from the distant past and the latter being a ship from the distant future.
Spock ends up teaching Scotty his own formula for transwarp beaming in order to get Kirk and Scotty to the Enterprise. Since this universe is already greatly out of sync with the previous one this doesn't actually cause a paradox. In Star Trek 4 Scotty ends up teaching someone from the past how to make transparent aluminum and suggests that he might have been the one to invent it. This possibility created what has been nicknamed a "bootstrap paradox" meaning that the item/theory in question has no origin apart from being brought back in time infinitely. Star Trek 4 also saw Spock witnessing Kirk selling his antique glasses in the past with the thought that those exact same glasses would be given back to him in the future.
When Spock and Kirk head to their final confrontation with Nero, Sulu is left in command. While he seems to find the Captain's chair comfortable he also manages to rush in, torpedoes blazing, at a crucial moment to save Kirk and Spock. This is actually quite similar to his role in the final space battle in Star Trek 6.
Apart from Spock, none of the characters in the series were in the original pilot episode of Star Trek. This particular point is grasping at straws especially considering that there is a flaw in the logic. Sulu, Uhura, Kirk, & Scotty were not meant to be on the Enterprise during the events of the film but still managed to make their way onto the ship and become crew members. The flaw in this logic is that Chekov and Bones were both stationed on the Enterprise during the film despite not being in the pilot. Numerous reasons could account for this but it's obvious that absence in the pilot episode didn't determine their presence in the film.
This last fun fact is actually the most obvious seeing as it's central to the plot of the film. The order of which the characters were brought onto the Enterprise all played pivotal roles in surviving the ambush that took place at Vulcan.
- The sequence of events started back when Pike convinced Kirk to enlist.
- Fast forward a few years to when Uhura told her room mate about the attack on the Klingon fleet. Kirk overheard this but took no note of it until much later.
- Fast forward to the Kobayashi Maru. Kirk decides to cheat the test by changing the protocols to create a more favorable outcome. This infuriates Spock, who happened to create the test. Spock then has Kirk court marshaled and suspended from duty pending another hearing.
- Uhura uses her influence to convince Spock to move her from the Ferragut to the Enterprise. Had this not happened, she likely would have been killed as the Farragut was destroyed.
- McCoy (Bones) sneaks Kirk onto the Enterprise despite his suspension. It's possible that Kirk could have been assigned to a different ship had he not been suspended from duty.
- Sulu ends up replacing McKenna as helmsman and makes a mistake that delays the departure of the Enterprise.
- Pike orders Chekov to explain what is known of the situation via a video intercom.
- Kirk happens to be laying next to one of the monitors in Sick Bay, causing him to start putting everything together.
- Kirk confirms with Uhura that Romulans destroyed the Klingon armada then made it clear to Pike and Spock that they were heading into a trap.