In terms of story telling, I thought it was pretty weak. I'll probably end up having a bit of a rant, so long post ahead. Also, spoilers.
First of all, we've got that black guy with the sick daughter. What was the point of that? What did that entire sequence accomplish? The only things it did was to establish that Khan's blood could (somehow, it was never properly explained) cure illnesses, and that there was a bombing. None of this needed that family that we never saw again. The "Khan's blood is a magical cure" bit was better explained by the tribble sequence. And as for the bombing? Why did Khan go to all the trouble of having this guy plant the bomb if Khan was going to actually be there in the aftermath (as Kirk saw in the meeting)? Instead of going to all this pointless storytelling, just have Khan sneak in, showing how clever he is. Get's caught, has to fight a few guards (showing how strong he is). Plants the bomb, blows the place up. Establishes his character, shows his intelligence and strength. Sure, it doesn't do the "blood is a cure to whatever disease you might have" thing, but that was explained later in the movie anyway.
The first bit was good. Show Kirk saying, "Fuck you" to the rules, and then BAM he gets demoted. Force him to live with the consequences of his arrogance. That was a lot like Kirk from TOS. Making him a commander was also good. But then, as soon as Pike is killed, Starfleet says, "Oh well, we'll just make you a captain again and give you back the Enterprise." WTF is this? What was the point of demoting him in the first place? It would have been far better to have Kirk as Pike's XO (with Spock staying as Enterprise science officer), and then have Pike killed later. That way, Kirk has to EARN his command back instead of Starfleet telling him he might as well just have it back. Maybe have Pike die trying to fix the reactor. That would give Kirk a HUGE motivation to go after Khan.
Or, have Admiral Marcus take command of the Enterprise. He wants Khan dead, so why is he sending out Kirk to do it? Marcus takes command, goes after Khan, and then sends Kirk on the away mission to kill him. Marcus tells Kirk to kill Khan, but Kirk refuses, thus getting Marcus to turn on Kirk and revealing Marcus to be the bad guy.
And seriously, that scene with kirk fixing the reactor in the bit that they cut 'n' pasted from tWoK was just pissing on it. You actually telling me that something which KILLS a Vulcan in a horrific manner just makes a much weaker Human "just a little dead"? Seriously, WTF is this? And then, Khan's blood cures him. Did they stop off at Miracle Max's? "To BLAVE!"
This is so cheap. It's like when they are fighting the neural parasites in TOS and blind Spock - But Spock has a magical inner eyelid so everything's okay! Or when they try to give Worf a new backbone and he dies on the table - But Klingons have redundant body systems, so everything's okay! Last time someone died this way, they had to spend a whole movie trying to get him back, at great cost. Now they fix it in five minutes.
Which brings me to that whole big fight thing. It's Kirk's movie. He's the one who gets demoted. He's the one in command. and yet, in the big finale, Kirk's on his back and Spock's the one solving the problem. Why? I mentioned before that you could have had Pike die in the reactor (and stay dead). Then you could have had Kirk fighting Khan instead of Spock, and no need for that crappy, "We need him alive" stuff either. It's a movie, Kill the bloody villain.
A few final thoughts...
Why was Khan using a fake name anyway?
How does Kirk, sitting in Klingon space, talk to Scotty, in the Terran system on a freaking communicator?
Seriously, what is the range on these things?
And that big ship, Vengeance or whatever... That was the biggest fanwank I;ve ever seen.
All in all, I was quite disappointed.