Non-spoilery: I really enjoyed it.
The movie is quite relentless in it's pace, there's barely time to breath, but lots and lots of laughs. The banter between the main characters is absolutely delightful and adorable. I was pretty much laughing through-out all of it. So quite unsurprisingly this is actually their take on Star Trek II, which is absolutely fine with me. I'm glad they did not kill Cumberbatch's Khan, because he was stunning. Sadly there wasn't much new footage of him in the movie because pretty much all of it is in the trailers. Yup, that's quite a disappointment. I really liked that they (inadvertently?) showed that the crew of the Enterprise is not so different from Khan. Kirk's reaction to Pike's death (noooooooooooooo! I really liked him!) and Spock's reaction to Kirk's death weren't so different to how Khan reacted. Okay, they did not kill thousands, but they were out for vengeance all the same. They had someone to stop them though, which Khan does not have, so maybe that's the difference. I think I might have preferred if they had stranded him and his crew on an uninhabited planet like in the original series. Just putting him on ice seems so... I don't know. I do hope they at least told him that they did not kill his crew. If they had told him before he sank his ship in Starfleet headquarters, they might have even prevented all these deaths... really... okay, maybe his coms were down after the explosions, but they could have mentioned that at least.
I liked all the little and not so little nods to TOS (I'm sick of writing the original series). The one with Nurse Chapel was especially nice. I really liked how they twisted the sacrifice of ST II and how Kirk told Spock that it was "the logical choice" :) Sadly my boyfriend spoiled me by pointing out the dead Tribble with Khans blood when Kirk went into the chamber (I was like "Oh no, they didn't!!!"). That really killed the scene for me :( The girl next to me was crying her eyes out and I was shooting laser beams at my boyfriend for ruining it for me. I managed to be completely unspoiled and then he pulled this stunt on me... damn him for being so perceptive!!! Of course I knew about the damn Tribble, but I had blissfully forgotten about it by the time Kirk went into the chamber!
Honorary mention goes to the absolute starship porn. Oh god, they really gave us some amazing goodies in this movie. I was frothing out of my mouth from starship envy...
One thing that gets criticized a lot is Spock's crying. I don't think it's ooc for this Spock. He's different from the Spock we knew, he saw his mother die and his home planet being destroyed. He had a near death scene in that movie and saw a man he respected a lot die, feeling what he felt. And then his best friend is dying and there's nothing he can do. This Spock also has a lot more sass, he's quite good in saying one thing and meaning quite the opposite. I like this new Spock. Come one, with old Spock we always waited for him to betray emotions, with new Spock they're a bit closer to the surface, I like that.