My fear is that the "epiphany moment" for both emotional Spock and cocky Kirk that causes them to change their ways will not be a believable one. I think it would be very difficult for this film to capture the "maturization" of BOTH of these characters in a believable way -- even doing that for one character is a challenge.
Although, perhaps the maturizataion of Kirk and Spock are intertwined with each other in a very coherent way -- meaning that each character needed the other to help them become the person we know from TOS. THAT would potentially be a very interesting aspect of this film
This has been my fear, too. That and dealing with the backstories of five other characters. Someone is going to get short-shrift. Developments may happen too fast to be believable (even after suspension of disbelief, which I routinely leave in the car before entering any theater to see a movie). McCoy apparently becomes chief medical officer when the other one is killed. Kirk has to take command of the Enterprise from Spock after Pike is conveniently indisposed. My guess (fear) is the red shirt who buys it at the drill site was the chief engineer (maybe not). That would mean Scotty moves in by dead man's boots, too.
As Jackson said, Kirk has a lot of growing up to do in this movie. And Spock seems to have major issues, too. It may be too much to ask that both are resolved by the end of this promised to be "action-packed" movie.
So I guess in sum, my fear is this movie/story bites off more than it can chew.