First off, I think Jimmy is a sophomore because early in the game he says he is 15. He could've been a Freshman and been 15, but it happened early in the game so I assumed he was a second year.
Secondly, the problem with Bully is that it doesn't have a branching/faction based storyline. They should have it where you can actually pick which clique/storyline you want to do and have the world revolve around your decision.
Thirdly, I would like to see more time put into the combat. I would like to see weapons/attacks be more useful and precise like the boxing match fights. While I wouldn't want to add complexity to a brawl system I think it'd be better served to have a little bit more depth. Yakuza, a game somewhat similar to Bully, had an excellent fighting system that still retained a humorous/thug like style that I think the Bully creators wanted to make.
Finally, I would like the game to focus around the school only. The reason for that is because the City missions only added more places to visit and didn't really have a purpose other than to extend the game deeper. If you focus on the school you can put more secrets in the school and more events in the school and make the school a bigger part of the game. I wouldn't be opposed to finding a town late in the game, but only late in the game, and have it be difficult to get/explore because of school rules prohibiting it.
I also have some problems that I detailed in my thread "Problems with Bully" that I think are microo-problems that could be fixed to the overall Bully formula.