Basically all you said, along with some others like umm... Random bad things happening around town... so you might be driving around and a police car or ambulance goes speeding by trying to get somewhere else or something
And motorcycles... I wanna ride motorcycles
ummm... I dunno...
Oh and Police chasing you while doing vigilante missions still makes sense if you're driving around running over innocent people and blowing up other cars or something (even if it's accidental)... If real cops did that, they'd be arrested to, right?
That would be awesome if they made it so you could choose what gang you're in... and you're appearance would be different depending on which one you are in, and like there would be a number of different gang-related missions that would be different for each gang... And maybe as you like rise up the gang ladder and get more power or something, you could eventually like go to some place and get a few other gang members to follow you and you could run into another gang's territory and have a big shootout or something...
But yeah bye.. I doubt there will be such major additions... maybe GTA4 though
Oh wait, how could I forget! 2 player mode... You could hunt each other down, work together, or just run around and do your own thing...