Mine would be as follows:
-Have different swing animations (as seen in the comics). This also applies to the movies. I know you could buy moves that you could do after you swing in spider-man 2 the movie, but I would like to see moves that you can do while swinging to further increase the fun of web slinging.
-Have a storyline in where you can change your future (like fable). For instance have spidey find the symbiote costume, once he does you can either turn into venom yourself (bad ending), or get rid of the suit (good ending). Some things that you could do that would have you become good or evil is to save someone or let them die. Hurt criminals too much (using pressure sensitive buttons for example), where you could either knock them out, break various body parts, too outright killing them.
-focus on fine tuning the combat system.
-Have more secrets such as costumes, different characters, special stages where if you collect a comic (scattered around the city), you can play that scenario in the comic.
-I'm not too sure on this, but implement some sort of levelup system. So that you don't have to buy them (will in turn make the experience more realistic by growing through practice). For instance, every so often you can gain extra jumping power, speed, accuracy with your webbing, etc.
-If indeed the next game will be based on the ultimate spider-man comics, have an extra mode called "comic mode" where the cinemas are like the ones found on the comic-dvds. Since Mark Bagley is a fantastic artist, it couldn't hurt
-The final thing I can think of is to include the older spidey games like spider-man vs. the kingpin (my favorite), maximum carnage, spider-man, and any others that they can get access too.
What are your ideas?