I've seen the movie 5 times now and I seem to find something new every time. A couple things I wanted to mention and didn't see any other posts on them.
First when young Spock is answering the questions on the Vulcan test, I believe one or more of the answers are the same as answers from the questions at the beginning of STIV. Did anyone else notice this? I have to rewatch STIV to get the questions and answers to compare
Second, after a few times seeing it, I remembered that James Doohan's son Chris had a brief cameo in the movie. I had to look up on the internet to find out the scene but he plays the assistant transporter chief. I noticed him in the scene when Scotty beams up Kirk/Pike and Spock.
Also, I did see the Vulcan ship from First Contact when Spock is flying out of Nero's ship, just before the scene where Kirk finds Pike. I think one reason that Nero would have this ship is that he may have had a Vulcan fly aboard his ship at some point. Either before the attack on the planet or sometime much earlier. Just like he did with Pike and the captain of the Kelvin. Those shuttles must be like his trophies or something??