Lots of witty banter.
Not as much lens flare as the first one.
Still more lens flare than there ought to have been.
Some people thought it was being too referential to parts of the original series. Or perhaps "too pandering" is the right term.
JJ Abrams (or whosever's responsible this) still has a tendency to paint himself into a corner, then whip out some fancy new technology to solve the problem without apparently considering the long term effects of that technology. (cf. transwarp beaming from the first movie.)
Rob Bricken, of ex-Topless Robot now io9 fame, has put together one of his usual Movie Spoiler FAQs. They're wonderful when you don't like the movie in question, but even if you thought the movie was fun they usually point out some real flaws in a humorous manner, and i agree with a lot of his criticisms in this case despite my general thumbs up.
On a related note, someone tried to specifically access the scientific accuracy of a lot of the stuff in the film here: http://trekmovie.com/2013/05/18/the-science-of-star-trek-into-darkness/
So, on to the spoilers!
So i'd heard the rumor that Cumberbatch was going to be Khan, then i'd heard the rumor that no, he was some guy named "John Harrison", so i wasn't sure what to think. (Clearly leaking his alias was a good PR move as far as keeping people guessing, although that in itself seems to have pissed some people off.) Yet somehow, despite mentioning the Khan rumor right before going to see the movie, i somehow immediately forgot about it for the first half of the movie, though i did remember again just slightly before the reveal. Part of that i guess is that Cumberbatch doesn't look anything like Ricardo Montablan (and i'm sure there are a number of people unhappy about a major non-white character that was played by a non-white actor being replaced by a white guy.)
I admit that when the got to the underwater Enterprise part at the beginning my immediate thought was "why did they put a ship designed for -1 atmospheres in a situation where it must be experiencing at _least_ 6 atmospheres of positive pressure?) I then said to myself "it's just the intro, it doesn't really matter so screw it" before i even got to considering the resistance of trying to move the ship through that dense a medium or the physics of trying to get engines designed to operate in space to work underwater.
I also confess to having mixed feelings about all the references to old Trek. The reactor scene and the "Khannnnn!" bits in particular were simultaneously cool, amusing, and just cheesy.
The ability to regenerate people using synthesized Khan blood seems like one of those stupid overpowered ideas that will be stuffed in a closet and only pulled out when they need a last minute fix to a problem and never applied on a systematic basis. Just like transwarp beaming. Which notable only got used once in this movie when they needed the bad guy to get around quickly. They say it was classified by the military which would explain why it wasn't in use by the public. However in "real life" i would expect that if the Klingon war had gone off as planned, then about five minutes after it started every shipyard, naval base, and anything else like that would have found dozens of photon torpedoes beamed either directly inside of or (in the case of shielded targets) right next to the facility from light-years away. But that will never happen.
And speaking of that, i think the "Into Darkness" subtitle was a bit overblown and melodramatic. We didn't really see that much of a journey into darkness, and it was pretty much all wrapped up by the movie's end. In the middle i was expecting war with the Klingons to start, and toward the end i was expecting Khan to get away, with or without his crew. In other words i was kind of expecting this movie to be a trek _into_ darkness, and then the related sequel would deal with the darkness and potentially dig its way out again. But nope. I guess "Star Trek Into Mild Dimness But Don't Worry It Will Be Bright Again By The End" just isn't catchy enough.
I suppose it's possible the events of this film will in fact trigger a war that will get dealt with in the next movie, but if so it wasn't really a thematic part of this movie in the way that i would expect to justify the title.
But i reiterate, it was a fun movie, it just seems like it takes a little too much from modern/current/whatever film mentality. Just throw some shit in there because it seems exciting without paying attention to the long term implications. (There's a bit of angst amongst nerdy fans about exactly how long it takes to get from Earth to other planets and back again. JJ Abrams' sense of dramatic haste seems to have soundly trumped canon.) The result is exciting when you watch it, but may not hold up as well over time. But i guess that is something that only time will tell.
I know that they made shit up all the time in the old Star Treks, but my vague (possibly nostalgia influenced) memories claim that it wasn't usually stuff with such wide reaching implication. "Bouncing graviton particle beams off the main deflector dish" just isn't quite the same as "we can teleport between interplanetary distances now, including between targets moving at warp", "we can warp between different solar systems in hours or less" and "[spoilery thing]"