Some aspects were handled very well indeed. Some were not. Most were at least adequate. It's more action-oriented than most Trek, but even so there is still a lot more to the movie than the continuous series of explosions which the trailer showed.
Overall, I have to say the good outweighs the bad and declare that this was a decent movie and a decent addition to the Trek canon, which is not at all what I expected to be saying.
Chekov and Uhura get more respect in this version, Scotty gets less. I can't fault Simon Pegg for that, the part was obviously written with his talents in mind and I don't blame him for taking that and doing what he does best: comedy. Scotty always did have a comic side, but he could also be quite serious. We'll have to wait and see whether Pegg can fill those boots all the way. The new Doctor McCoy seems to be possessed by the ghost of DeForrest Kelley at times, it's uncanny.
Major points for providing an in-story explanation for the reboot!
Spock isn't nearly as boy-band pretty as I thought from the trailer. He doesn't have Nimoy's deep voice or the gravitas that gave him, but he shows promise. He is also written as more accepting of his human side than the original, who was very very Vulcan through the series and only grew beyond that in the movies -- so he doesn't need quite the same level of dignity, either. Kirk is pretty, but I think that's just because he's so young. The entire crew is, either still cadets or just graduated, except for McCoy, who is visibly older than the rest just as he was in the original crew.