First, this was the most fun I've ever had with a Star Trek film. Hands down. The crack someone made about this being the first /real/ movie of "that 60's show" is spot on. This honestly feels like the first real movie of Star Trek to me, because, perhaps, the creators of it were not /too close/ to the property to not miss the forest for the trees. This is the movie made, not for "the casuals" as some hardcore Trekkies like to believe, but rather, for people who enjoyed Star Trek as entertainment - not quite as much for people who fixated on Star Trek as an alternate fictional reality like the hardcore fan tends to.
The key thing about the film for me was this: there was chemistry among the cast and most of the time it crackled with energy. The whole movie is alive with energy and it's infectious. For an ensemble piece like Star Trek, having a cast that is "alive" as a group is the most important thing.
Next, the screen writing was very cunning I felt in that the writers seemed to be clearly aware when they were dealing with stereotypical Star Trek scenarios. Time and again, they'd have the characters edge towards the 4th wall, turning a classic Trek dialog exchange on its head, sometimes for dramatic effect, other times for comedic. Kirk's romp in the Kobyashi Maru scene was priceless, and the scene at the end where Kirk and Spock face down Nero on the viewscreen - every line is knowingly a play on what Star Trek at its most stereotypical and lifeless would trot out. I realize some object to Kirk's eagerness to blow Nero away, but I felt it was perfect in context of all the hell that everyone had just gone through. This was after all, young, unseasoned Kirk, at his most brash and headstrong.
After all that, I really appreciated the visuals of the film. There was at times perhaps a bit much shakey in some moments but it wasn't as bad as the shakey-cam allergic made it out to be. What I appreciated was a strong sense of trying to make things real, with a sense of being there, crazy lens flair and all. I also appreciated how punchy everything was, from the practically gunshot warp drive initiation effects to the intense sizzle and crackle from energy weapons fire in close quarters.
The one thing that did let me down a bit was the downside of who wrote the movie and how they wrote it (everything has a downside, no matter how good). The Trek Science bits involved with explaining the backstory, as given by Old Spock, were pretty terrible, with offhand mentions of a single super nova that "threatened the galaxy" and no explanation whatsoever that Spock would have known how to use a black hole to achieve time travel - making it seem as if the /regular result/ of just randomly diving through a black hole is time travel. The thing is, certain details like this are recognizable enough to even laymen and casual viewers to seem hokey and silly. While it's granted that Star Trek has things like warp drive and transporters, those things are science fiction Black Boxes: additional rules to the laws of physics that some unknown technology is capable of manipulating. People will accept that and it won't grate.
Despite the terrible science (fiction) writing at a few key points, overall I felt what we got was damned fine and the best general space adventure film, well, since I'm not sure what. It's been a while.