I want to see Bruce establish a friendship with Gordon. Due to Batman's status as a wanted criminal Bruce will obviously want to make up for his lack of activity as Batman by funding projects in Gotham. Through this I hope friendship will grow between the two.
I want to see Bruce's faith in himself restored by the presence of Black Mask. Something I've noticed from the last two films is that Bruce doesn't really want to be Bruce, he only wants to be Batman. Through observing Black Mask Bruce should realise that it's his character that makes him who he is.
Personally i dont think they should ever come closer than they already are. In the comics Gordon probably knows but blocks it out and pretends that he doesnt. I would only like them as friends in the distant future, like how in Batman Beyond he and Bruce would meet every year in old Gotham where the GPD headquarters used to be (now its an abandoned building) and have a cup of coffee.
So, what would i like to see?
1) More comic book atmosphere to the whole movie, like the one we had in Begins.
2) That would reflect in the BATCAVE: Huge, with catwalks over the abyss, with an underground river/lake, with many bat vehicles, a huge computer, a room for memorabilia, and of course the T-Rex. There best be a T-Rex there Nolan!!!
3) A better batsuit that isnt robotic.
4) Bruce in front of the bat computer in full costume, but with his cowl pulled back, like how NiteOwl did at the end of Watchmen.
5) Tumbler 2.0, Batwing and Batboat. Even if he doesnt use them in the movie, have them parked in the cave.
6) Firefly as a secondary villain (i dont know which one i'd like as the primary villain) and a big aerial fight over and between skyscrapers with batman gliding and using his grapple gun vs Firefly flying.
7) Akham Asylum opening again and Batman visiting. Joker and Crane cameos. Even if its just a laugh and a shadow from the Joker.
8) MOVIE REVOLVING AROUND BATMAN!!!