If you just want the quick advice about whether to see the movie: if you liked the first, you'll like the second, but don't think too much about the plot.
Here be spoilers.
If I was revising the script, but had to keep to the basic outline:
1. I would've made Pike the bad Federation officer so Kirk would've had to defeat his father-surrogate.
2. I would've made the new woman a Security officer because she was too blatantly redundant, especially for a character who may be returning.
3. I would've ended the movie with Spock outsmarting Khan rather than beating him up. Emma suggested moving the bit with the torpedoes to the end, because it did a nice job of showing how Spock can be honest and tricky.