The quick review: Heaps of fun, but too much Old Spock and not enough Uhura.
And why didn't they change the sex of any of the characters? There's a fine answer at The Panopticon: Do Gay Martians Have the Right to Marry?
That out of the way, spoiler alert!
If I'd written the last draft of the Star Trek movie, I would—
1. Make Chekhov female.
The rationalization is easy: he was born a few years after Nero's alteration to the time line, so "his" moment of conception could've shifted, even just an instant, and the genes would unite differently. (This isn't to slight the actor they cast, who was great.)
2. Add more Uhura.
In the bar, she should enter the fight against her fellow cadets to help save Kirk—which would make him have an even bigger crush on her. There should be a scene where the universal translator misses something significant that Uhura catches to save the day. And when Spock and Kirk beam aboard Nero's ship, she should come along—having a Romulan speaker would be awfully useful—and get to do some buttkicking there.
3. Leave Old Spock in the future.
I might keep a cameo of him as Nero explains his motives. Otherwise, Old Spock's presence weakens every plot point he's in so much that I wonder if he was added in a late draft.
a. On the ice planet, Kirk should be saved by Scotty and Scotty's alien buddy.
b. Scotty should figure out the necessary equations without help, damn it!
c. When Kirk meets Spock on the bridge, they should argue simply because that's their nature. Spock loses it, then gets control of himself (maybe after Uhura knocks him aside?) and turns over command of the ship. And that moment of Spock doing the right thing under pressure should be Kirk's moment of realizing that Spock is an amazing person who should be his friend.
d. At the end, Spock should say farewell to his father, not his older self.
Even so, I was happy enough with this movie that I look forward to the next. Yes, the science was silly, but when you're accepting faster-than-light and time travel, you shouldn't quibble about red matter.