1. The movie is too damn long. The first 20 minutes of the film could have been done away with without out taking much out of the story and making it less ridiculous, especially since because of what occurs in the first 20 minutes, Kirk is demoted and then reinstated within about 15 minutes of screen time later. Makes the Starfleet organization seem really messed up.
2. Not enough Cumberbatch. We only see glimpses of him in the first half of the movie and even then not enough of him in the second half. I really have no idea why Spock could rightly say that Khan betrayed the Enterprise. Poor guy is the one who has been shafted throughout the movie. First when he is woken and his crew held hostage. He then gets the crap beaten out of him even after he has surrendered. Later on he teams up with Kirk and Scotty only to have Kirk backstab him at the end. Khan just seems to be reacting to how he is treated. Not condoning what he did at Starfleet Headquarters and Section 13 or denying how savage he was aboard the bridge of the Vengeance, but are we supposed to just take it for granted he is the epitome of evil just because his name is Khan and Old Spock says so?
3. Kirk is an ass. He can't stop harping about how he saved Spock's life. What a prick. I wouldn't want him saving my life.
4. The plot holes become even more glaring on the second viewing, if that's actually even possible. Lots of physic holes too.
5. Didn't really appreciate Simon Pegg's Scotty enough the first time around. Appreciate him a lot more in the second viewing. Will be sure to check out more of his other films.
6. What's with all the weak female characters? Uhura basically serves as Spock's love interest. Dr. Carol Marcus's idea of disabling a live torpedo is just to rip the whole thing out. And she strips down to her undies for a flimsy reason. Even though there are a few female officers at Starfleet headquarters, you get the impression that there were only men present there. Guess women still haven't achieved equality even centuries into the future. *Sigh*
7. Just a tad disappointed that the scriptwriters actually recycled quite a huge chunk of Wrath of Khan for this movie. You would think that in the 4 years between Star Trek and Star Trek into Darkness, they would have come up with something more original, especially since they created an alternative universe in the first rebooted Star Trek movie to get away from the canon in the first place.
8. Magical blood, really? One finds it hard to care for the characters if we know that none of them are ever going to be in real danger.