What everyone else is saying. What really defines Star Trek? To me, it's how the characters deal with the challenges they face. It's not the size of the screen, the explosions or even the villains. It's what the characters do and how they act..
Star Trek is, in part, about the characters. One of my disappointments in the new Trek is that our heroes have been largely reduced to their pop-cultural images. McCoy's role is not simply to crack wise, but to raise important moral questions. That stated, it was nice to see Scotty conscientiously object to Kirk's mission. I think Pegg is growing into his role nicely.
I think the greatest improvement that could be made would be to ground the action in a stronger story. Instead of having a string of action sequences with a revenge-driven villain, it would be nice to see a Trek movie centered on ideas.
The movies have tended to be bigger and dumber than the television shows, in general, but I don't think that has to be the case. I think they can do everything that they are doing well in terms of action, pacing, quips, etc., but add a little more heft.
Bones had more character-building in the last film, so I think Scotty getting his turn was good to see. I thought the action drove the movie along at a good pace, and the themes of terrorism and the response we can have to threats really echoed what we struggle with in today's society. I don't see how these characters are reduced to "pop-culture" when they are completely different from the characters we knew in all but personality. There's a base, but it has to be built upon.
I thought the story was very strong, because it is Kirk's story- he grows up throughout this film, dealing with demotion, the loss of his father figure, and then becomes so driven by revenge he doesn't listen to others or stop to realize what he's gotten his crew into until it was too late. He knows that he is playing with fire in regards to Khan, but he has no choice.
Sure, Marcus could have been a stronger character, but really he was just the driver of the story...he gets the plot where it needs to be, but stays out of the way for the most part. I really liked what they did with Khan's character. He is manipulative and malicious and much more intelligent than the original Khan was, imo.
I loved the homage scene, and never felt that it was ripped off. I felt that it completed Kirk's character arc, which nothing else would have done- he had to learn sacrifice. It also serves as a catalyst for these two people to become friends for life. It's so different in theme and meaning that it just doesn't feel the same to me.
That's why I liked this movie. I could nitpick it, but I try not to because then I would never enjoy anything.