For starters, the film was fast-paced and entertaining. I don't recall ever being bored. One goes to movies to be entertained, after all, and this one did a good job.
Secondly, it was great to see iconic Trek baddie Khan Noonien Singh back in action. The reboot of the Star Trek franchise (well, with the exception of stuff like Enterprise that takes place earlier) allows for the best stories of the old universe to be done again and Khan was among the most terrible enemies the Enterprise has ever faced. He would have won in "Space Seed" were it not for Lt. Marla McGivers' attack of scruples and made the named characters (as opposed to the disposable red-shirts) bleed the most--in Star Trek II: The Wrath of Khan he killed Scotty's nephew and (temporarily) killed Spock. And he's a complicated character in his own right, not some one-dimensional killing machine.
Although I would have rather an Indian actor (or at least someone who could pass for Indian) play Khan, Benedict Cumberbatch did an excellent job. I liked his speech to Kirk when he reveals his identity and how the Federation needed a warrior and a savage like him to fight the Klingons. Khan is supposed to be charismatic and that speech works. And he has so many great lines ("no ship should go down without her captain") that he delivers so awesomely. And apparently Cumberbatch was willing to learn how to fight hand-to-hand as well, something he shows off taking on waves of Klingons (and some of their ships) while dual-wielding some very large guns
Speaking of that, I liked how all the baddies had reasonable motivations. Admiral Alexander Marcus wants to militarize Starfleet and after the events of the first movie (in which a Romulan ship from the future destroyed many ships and the entire planet Vulcan), that's not completely unreasonable. The original series featured the Klingons as the Federation's great enemy, and that was without the enormous losses the Federation took at the Narada's hands. Marcus points out the Klingons have seized two worlds--with the Federation damaged, I imagine they'd be more aggressive than they were in canon. If the Federation's peaceniks are still in charge, Marcus trying to do things on his own--like finding the Botany Bay and employing Khan, who described himself as "an engineer of sorts" when introduced in "Space Seed" to covertly advance Starfleet's weapons program--makes a lot of sense. And Khan, who views himself as genetically-superior to Marcus, no doubt rankles massively at being forced into servitude, especially since Marcus is using the last remaining (to Khan's knowledge) Augments as hostages.
The movie also does a lot more with Uhura, which was really cool. I particularly liked her interactions with the Klingons.
Also, like its predecessor, the film has plenty of humor. In particular I liked Scotty and his little alien sidekick, plus the scene where Chekhov is assigned to engineering and given a red shirt was funny.
I didn't mind call-backs and references to earlier "Trek" material, or even references to previous adventures featuring Khan. However, toward the end of the movie it started getting ridiculous. Kirk's self-sacrifice to save his crew is identical to that of Spock at the climax of Wrath of Khan, even down to the touching-hands-through-the-glass part. And this time it's Spock screaming "KHAAAN!" That came off as unintentionally hilarious. Plus the reason Spock sacrificed himself was that he was the most physically durable of the bunch and could withstand the radiation in the core long enough to get the drive functioning again. Kirk would probably not have been able to do that in the first place.
Once I began to suspect the villain would be Khan and he'd be played by Cumberbatch, I got mildly irritated. Khan is supposed to be northern Indian, a Sikh specifically. The original Khan, Ricardo Montalban, wasn't Indian, but he was darker-skinned. Cumberbatch is VERY white. Cumberbatch did a great job, but I'd rather have someone of the proper race playing the character. Hollywood has a not-very-pleasant history of racial miscasting--in my "ethnic cinema" class in college, I remember reading about how a great Japanese actor was denied a part in a movie in the 1920s because everyone else was played by white actors in heavy makeup and he'd stand out too much. I'd suggested Hrithik Roshan play Khan, since he's a major Bollywood star who looks the part. The only major Indian actor I can think of who's well-known in the U.S. is Kal Penn and he seems too young, plus the fact John Cho plays Sulu risks people calling this "Harold and Kumar Go Into Space" and that'd be a strike against the movie from the get-go.
There's also the problem of knowing just who Khan is. When Harrison reveals he is Khan I knew who that was, but the movie doesn't go into detail about why he's such a bad guy. Terrorists are a dime-a-dozen, but evil overlords who once ruled a quarter of the human population and are now back to wreak even more havoc aren't. Comments from Khan, Marcus, and both Young and Old Spock drop hints, but more exposition through dialogue or even a flashback to the Eugenics Wars would have been better. That would have involved dealing with the nature of those wars (most of the ST expanded-universe material makes the EW sound like a world war complete with the original U.S.S. Enterprise being destroyed in battle with a nuke, but a pair of novels attempted to make the events of our 1990s the result of Augment machinations), but it could have been really interesting to see the last days of the Great Khanate, the launch of the Botany Bay, etc. In the second "How I Would Have Done It" post, I recommended introducing Khan at the beginning of the film in a Eugenics Wars flashback, only played by a different actor so the big reveal would still work.
(Plus when Khan was introduced in "Space Seed," he got a mixed reception from the Enterprise crew, some of whom outright admired him. In the film, Young Spock calls him a genocidal monster bent on exterminating all he deems inferior to himself, something Khan doesn't deny. Although Spock in "Space Seed" is the one most skeptical of Khan's worthiness of admiration, I don't think he hated Khan like that, nor was Khan that blatantly monstrous.)
Also, although I'm quite willing to admit Alice Eve is good-looking, the scene where her character Carol Marcus strips down to her underwear was gratuitous and stupid. I know from canon that she and Kirk will get together and she ultimately bears his son, but non-Trekkies won't. This scene got on so many people's nerves that one of the writers even apologized for it, which is a pretty big deal.
Overall a good movie, even if the plot could have been more creative. 8.0 out of 10.