The biggest problem with SR3 is the actual sandbox itself. Steelport is boring and there's far less to explore than in SR2 Stillwater. So a better sandbox, wherever and whatever city it may be, should be priority number one.
After that I want to see a return to SR2's melee combat system since it was far more satisfying. Maybe keep the finishers from SR3 but make them rarer, possibly implementing a power up meter that build as you use regular melee attacks and when full allows you to use running finishers. A return to layered clothing would also be great since it allows for better customization (and on a sidenote, bring back sling bikinis lol). They also should bring back all of the missing activities like Fight Club, Fuzz, Septic Avenger, etc. and make them SIDE MISSIONS, not including activities in the main storyline like Sr3 did.
Hopefully Jason Rubin gave the team a good kick in the pants but at the same time his comments about the humour of SR3 make me nervous that he might have influenced them to make the game more serious, which would be a horrible mistake.