This is a pretty long list, but it is what I would like in SR4:
1. Being able to replay missions and cutscenes. How could you leave that out?!
2. Instead of there being one powerful criminal organization that is separated into 3 parts (the Syndicate), let there be 3 separate gangs that do not work together like in SR1 and SR2.
3. Make missions more fun and creative. Mix it up once in a while!
4. Have better dialogue. SR2 dialogue was so much funnier and more witty than in SR3. Enough with the corny sex jokes!
5. Have a balance between the seriousness and the funny stuff. Like in SR2.
6. If Zimos is going to be in SR4, I want him to be in more cutscenes. I love that guy!
7. Crib customization that's similar to SR2. All the cribs looked different on the inside in SR2. Why is it in SR3, the strongholds looks the same like Safeword and the Casino. Please DON'T do that in SR4.
8. Don't force us to play activities. That was frustrating.
9. Bring back some of the activities from SR2 like Fight Club and Septic Avenger. Those are WAY more fun.
10. Don't bring back Gang Operations. Those seemed pointless to me. I liked the Stronghold missions in SR2, and I would like something similar to that.
11. Hydraulics in cars, like in SR2. You can't go wrong with hydraulics!
12. Have better graphics. Some parts in SR3 looked low-res.
13. Have more melee weapons. I would love for pepper sprays and shock paddles to come back.
14. Can Shaundi be a little bit more mellow in SR4? I didn't really like her being so uptight and serious. It really didn't suit her.
15. Keep the gang customization that was in SR3. However, I would like for my gang to be able to drive in any car I want them to drive in like in SR2.
16. Keep the idea of "sub-bosses" like the brutes.
17. Bring back the different combat styles that were in SR2. One combat style is so boring.
18. Food. I don't want to die from getting shot at, so I want to be able to heal myself instead of hiding and waiting for my health to come back.
19. Please bring Johnny Gat back. How SR3 killed him off was stupid.
20. Make gang vehicles customizable like in SR2. I was disappointed that I couldn't customize Syndicate vehicles.
21. Improve co-op and multiplayer. Take out Whored Mode because that seemed pointless to me.
22. Make Pierce have some kind of dialogue when I call up other homies like Shaundi and Viola. How could you miss this?!
23. Tweak the player customization. If SR2 elements and SR3 elements were combined, I would be a happy camper.
24. I want to be able to tackle whatever gang I want to tackle, like in SR2. Going on a single path is so linear.
25. I want to be able to enter some buildings such as night clubs and hotels like I was able to in SR2.
26. Have some minigames like Zombie Uprising. I'm not saying that there should be a Zombie Uprising in SR4, but there should be a variety.
27. Bring back some of the diversions in SR2 like ho-ing and ambulance diversions. Those were fun.
28. It would be interesting if I can be able to go back and forth between Stilwater and Steelport. Two cities to explore could mean more fun and mayhem for me!
29. Bring Dex back. I wanna kill that sonofa...
30. Stop with the pointless DLC that involves having special homies or clothes. I want DLC that expands on the story darnit!
If I missed anything on this list, feel free to add to it. After all, these are just suggestions.
EDIT: 31. I can't believe you guys at THQ and Volition scrapped the auto-tune voice option. That was genius! Add it in SR4!