I would be interested in more emphasis on internal custom characterization, like a dialog tree from Mass Effect or Alpha Protocol. Depending on who you're working for at the time, you could alter your discussions to match what that personality type is looking for in a soldier, and thus be granted with more information about each mission. It would be kind of like in Assassin's Creed except it would take place through conversation rather than faffing about for 50 minutes repeating the same three side quests. It would also kind of be like in Indigo Prophecy when interviewing the waitress at the beginning of the game, what questions you choose to ask will garnish you different results, with a proper string of questions that gives you the best ending.
This same mechanic could be used in other areas of the game, like if you were arrested by the cops, you'd be put in an interrogation room and depending on how well you do during the interrogation would alter the repercussions. If you did phenomenally well you were released and all of your items would be returned to you (yes it's not the most realistic depiction, but this is the GTA universe), or if you completely failed you'd be booked and loose a couple of in-game days which could result in mission failures, missed connections, suspicion from bosses, and a whole lot of other consequences that could affect your game.
I was one of the weirdos who actually really enjoyed the character bonding moments in GTA4 where someone would call you up and you'd go out and do something. I felt that it helped with the immersion of the game as well as fleshing out the character's back story and helping them become more memorable. I remember when I had to choose between killing Francis or Gerry McReary and I was actually worried that if I made the wrong choice, that Kate and Packie McReary would not want to have anything to do with me anymore. I found it quite amazing that a game like GTA4 actually had me caring about NPC's, when in most GTA games, the NPC's either die, betray you, or just disappear from your world.
Finally I think one of the big changes that would be interesting for the next GTA installment would be combining the game world during in between mission sandbox mode and mission mode. Blur those lines a little bit to allow players multiple options to completing missions rather than just gunning down everybody in opposition. Perhaps there's a character who needs to be killed and he likes to frequent restaurants in one particular section of town at the same time every day, you could then go around to the various restaurants and either:
A) Survey the place to look for openings
B) Bribe the owner to leave the back door unlocked, allowing you to bypass the target's security.
C) Go in gun's a blazing
D) Create a rapport with the target, convince him to leave (Much like what you could do in GTA4)
Essentially it would be nice to be given a mission, but given a wider time frame in order to accomplish it, to allow the player multiple paths to do it.
Basically all in all I'd like to see more RPG elements attached to the series because I think there is some potential for true greatness that GTA4 hinted at but never really fully delivered. My ideas would definitely drown out a lot of the rampage action, but I think if handled right there could be a lot of depth added to the series and allow it to give the players a more personal experience to the criminal underground, much like how The Wire did for television.