This is going to be a bit of a jumbled, out of order list.
Yorktown Station was so damn cool. I loved seeing its defenses when it tried to fight off the swarm.
Krall being incredibly Xenophobic after the Xindi and Romulans wars, and hating the Federation because he thought uniting with alien races was weakness made sense. I thought him thinking unity was weakness was decent enough motivation, but once they established his actual back story it made him a much better character.
I really wish the Enterprises destruction wasn't spoiled in the trailers. It would have made that sequence a lot better.
I didn't care for the shrunk down nacelles on the JJPrise, the swept back nacelles were fine, but the smaller nacelles didn't look right. Also didn't care the the neck being shrunk just so it looked more vulnerable.
The motorcycle sequence was fine. It wasn't excessive, and was only there to provide a distraction while they rescued the Enterprise crew.
All the references to Enterprise were fantastic. Polarized hull plating, spatial torpedoes, phase canons, the MACO, the Xindi war, the shuttle pods and uniforms in the video on the Franklin, all great stuff.
I liked that they pointed out that the transporter on the Franklin was for cargo since it was so old, and that Scotty had to modify it for use with people.
Pretty sure I heard them say the Franklin was lost in the 2160's right? That wasn't the date they said it was commissioned was it? Because if they screwed that up, i'd be a bit annoyed. I'll have to pay more attention to that scene when I see it again.
I'm assuming the majority of the Enterprises crew died, right? They only beamed maybe 3-4 groups of 20 to the Franklin and never mentioned having to go back for more. Initially when Kirk asked how many crew can the Franklin transport, I thought he meant actually carry, but they certainly beamed up more than that.
The Beastie Boys playing while the Franklin destroyed the swarm. It was a very cool visual sequence, the only thing I didn't like is the actual music. Destroying the swarm with a radio transmission was a cool thing, but I don't like the Beastie Boys.
Now, the whole Sulu gay scene. I felt they handled it exactly how Star Trek should have handled it. No one batted an eye, and it was a normal thing.
The Enterprise A. The building montage of that ship was amazing.
I need more images of that ship, I need them now. She looks like a good mix of the JJPrise and TOS Enterprises. The nacelles aren't bulbous anymore, but still taper. The Pylons aren't curved anymore, and just go straight out. I don't really remember the neck much. The deflector is the same as the JJPrises.
However there is one thing that totally ruins the movie, there is a disturbing lack of vests on all the civilians. We all know vests are the go to attire of the Star Trek universe, so them not being that just ruins the whole movie. (this was a joke)