The movie had many well done scenes, but I found it pretty lazy/weak on the overall storyline. I like the new actors and I think they all did great jobs. I can understand that no new movie is going to be 100% faithful to canon. The thing I disliked most was how they bent the rules of the Star Trek universe...a lot...to fit their storyline, and even then it didn't always make sense.
Some of these points have been mentioned, and some have been clarified a bit with Frogboy filling in info from the novel, but here were my issues:
1. No Supernova explosion is going to sneak up on a FTL race like the Romulans. It would certainly be dangerous to habitable worlds, but they have time to detect it and prepare for it.
2. You can't use a black hole to suck up the leading edge "shockwave" from a supernova. Too big. A black hole big enough to do this is more dangerous than the supernova itself.
3. Why is Ambassador Spock carrying 20 gallons of red matter when only a drop is necessary.
4. You don't have to drill into a planet to destroy it with a black hole.
5. The future Spock assisted transport across light years was conveniently far fetched even for the Star Trek universe.
6. Why did Nero and Spock get sucked back in time when they fell into the black hole? It would have taken very little explanation to say they were stuck in the event horizon and engaged their warp drives to go back in time rather than be destroyed.
7. Why was Spock's mother hanging out in the Vulcan elder sacred area? OK, I will give them a pass on this one to forward the plot, but seriously, she wouldn't be in there.
8. Why didn't Kirk and Sulu take phasers with them to attack the driling platform? Maybe Nero's ship would have detected the energy reading from phasers? So they had to take hand to hand weapons? (See, I'm trying to help them here!)
9. Ejecting the warp core would not have saved the enterprise from the black hole, it would have destroyed the Enterprise. They needed the warp core to maintain their speed, and the resulting proximity to the antimatter explosion would have destroyed the ship, not thrown it clear.
10. Delta Vega was not so close to Vulcan for Spock to watch his world get destroyed.
Finally the movie didn't feel that satisfying in that Nero was a villain who got very little screen time. The whole "save the Federation" plot felt incidental to Kirk being able to trick Spock out of his command. As someone pointed out, I also noticed Kirk got the crap pounded out of him in every fight he was in, though I suppose they weren't quite fair all being against superior numbers or stronger aliens. The old Kirk has always outwitted those he couldn't outfight, but he was a bit more of a weasel in this movie.
I would have liked to have seen Kirk be more of a hero so I felt like he earned that Captain's chair.
That said, it was an enjoyable special effects action movie with many funny, well acted scenes.