I agree that there's a number of bits that could be cut. The whole Kirk as Captain - academy - first officer - Captain again really added nothing to the movie and was essentially wasted time. As I said in another thread it felt like the writers response that Kirk was promoted too fast in the first one. However, when the whole arc takes about 5 minutes, what did it really accomplish? Have Pike express disappointment with Kirk, they go to the meeting, Pike dies and Marcus sends Kirk after Harrison. Plays out the same without the whole demotion bit. Same with Spock being assigned to the Bradbury. What exactly did that accomplish?
Wasn't really a fan of Carol Marcus. Was yet another set of daddy issues injected into a movie series that's already chock full of them. At least cut the connection with her and the admiral.
I know that a number of people will disagree with this but I'd also cut, or at least downplay, the Spock/Uhura relationship, II like seeing Uhura more involved in the plots but too much of her character is simply being Spock's girlfriend. The arguments, the making up, the abandoning her post when Spock's in trouble have Uhura being someon who's simple an appendage to another character instead of being one on her own. For a movie series that dreadfully short on women I'd like to see one who can hold her own against the males without being defined be her relationship to one of them.
Unfortunately, Star Trek is now a big, summer movie and there's not time or space for deeper characterization. We've got multi million dollar special effects sequences to show!
Just so you don't get the wrong idea. I enjoyed the movie for what it was worth. Hopefully the next reboot can take a slightly less frantic pace and let us get a bit more into the characters.