I think it's safe to say that I liked it.
I first saw it with T on Sunday, who isn't really a Star Trek person but was sucked in by the trailers, and today I was with
amybang, who is a bigger Trek fan than I am, and all three of us enjoyed it. As I said to both of them, if nothing else, it's so nice to have actually *good* new Star Trek content again, for the first time since DS9 ended (or since "Star Trek: First Contact", depending on what you mean by new). More action-oriented than most recent Trek, but since all the action advanced the characterization, the plot, or both (although it was more plot than character driven), that worked for me.
Bear in mind that I am definitely a Next Gen/DS9 Trekker -- I've maybe seen a dozen episodes of TOS, so most of my knowledge of those characters is from the movies (2-4 and 6). So I recognize that a die-hard fan of the original cast might have different impressions. But for me, it was pretty much exactly what I was looking for.
The Good: Casting. I thought pretty much all the re-casted actors were just about perfect. All the actors managed to walk that line of recreating the characters we know while still inhabiting them in a new way. The new Kirk is a bit brasher and more reckless than the old, but given the changes in his past, that makes sense. Spock was less controlled, showed more visible emotion, although most of his flashes of emotion came under extreme duress -- like Old Spock says, his homeworld was destroyed and his mother died before his eyes, so of course his emotions are running closer to the surface and are probably harder for him to suppress. But my favorite, hands down, was McCoy. What a perfect rendition of the character. Love him.
Also, I really like the way they handled the reboot: by setting this story in an alternate reality. So the "original" reality still exists on its old timeline and they can use the old continuity if they want, but there's now a whole new continuity for them to play with without worrying that they'll contradict something that came before. I kept expecting them to fix the timeline, bring Vulcan back, etc., but I'm glad they didn't. And I understand that this group is under contract for two more movies, so I hope we get the chance to see what they do with it.
The Not-So-Good: The fact that Uhura only really gets to do two things: a) translate a key transmission that is vital to advancing the plot... off screen, so we don't actually get to see her awesome skills in action, just hear her bragging about them and b) make out with Spock. I am really not sure how I feel about this Uhura/Spock thing. One the one hand, I do like that Kirk didn't get the girl -- especially since the girl was so determined to blow him off. I'm definitely glad not to have seen a classic "I hate you means I love you" turnaround. But I'm not at all convinced that it's in character for Spock to date a student (and I do think we were meant to assume that the two of them were together while Uhura was at the Academy), and I'm unsure about the choice to put the only significant female character into a relationship with one of her commanding officers. As long as it doesn't reduce her to "Spock's girlfriend" in future films, I guess I'm okay with it in theory, but it makes me nervous.
The WTF?: The Federation already knows that the Romulans and Vulcans are related? I thought that was a huge reveal in a TOS episode, which would have been a lot later on the timeline. Also, there is no way that Kirk's mother should have been on that ship -- families weren't on starships until the Next Gen era, and you can't hand-wave that one by claiming the changes to the timeline. Finally, I am amused that they sidestepped the whole "what do Klingons look like" question by not having any in the movie. A Star Trek movie without Klingons? What is this world coming to?
But if those are my biggest nitpicks, I'd say the mythology holds together pretty well. The science is another story, but who expects Star Trek to have coherent science? By this point, technobabble is as much a part of the series as the characters, so that doesn't bother me at all.
Long story short: two thumbs up, way up. And one of those is T's, and he's picky, so there you go.