I was a bit annoyed, as with the 2009 movie, with Chekov being on the ship in the 2250s, when he was only 10-15 years old (he was born in 2245). Sulu was born in 2237, so during the first movie, he should've been in the academy and not even have graduated yet.
I enjoyed Carol Marcus being there, but I wish there was a bit more sympathy, relationship building between her and Kirk to justify her line about being glad having a family, a bit more foreshadowing. Showing us Gary Mitchell in this film as one of Kirk's friends from the academy would've been really nice.
I still dislike this version of the Enterprise for having such a ridiculously small and misshapen engineering section that can't hold the huge brewery/engineering section it's supposedly got, and the warp core here apparently doesn't have any dilithium regulating the reaction.
I did like Spock's cameo, and the nod to Star Trek 2: "you'd better come down here. better...hurry."