Some things I'd like to see, in a little detail...
Large scale movable objects - ships are the obvious ones, but maybe other stuff too. You need the right environment to put them in but in GTA:SA it was possibly doable. To go with that you should be able to sink/destroy them with some form of reasonable modelling. Edit: oh yeah, car ferries, transporter trains, that sort of thing.
Large scale structural damage. The difficulty with this one is how it fits in with the plot. Suppose you crash your ship into the Golden Gate style bridge in SA, and do it some serious damage. How and when does it get repaired? Along those lines is possible demolition, arson and terraforming, but it probably faces more practical gaming problems than it's worth.
Proper controllable train systems would be good, with signalling, points and other sets travelling around.
I thought some form of 'build your own vehicle' might be an idea. Think Tanktics, if you remember that! You could have sets of components, i.e. pick a base - tank/wheels/hovercraft, a body, and features like a weapon or power etc and basically end up with a prototype that has handling characteristics based around those choices.
Improved helicopter and aircraft handling would be good - esp. partial loss of control when a helicopter's hit, instead of it just catching on fire.
More military kit might be nice; it's something only touched upon lightly in most GTA incarnations. It feels like there's more potential there. Civil war? Heh.
More character behaviours and random mutations thereof. Maybe traffic jams, road rage, random crashes etc, I don't know. Rarities and minor unusual events add value, I think. Longer term behaviours too - people with destinations or routes perhaps incorporating transport or parked cars. Just a little detail. Emergencies and responses independent of your actions might be an idea - it's all realism.
More stuff to do once the game is theoretically 100%'d. I guess this means events and randomised things that keep going on. Random mutations are the key again - things that are always slightly different to keep you playing. That's into game theory but I reckon you could easily automatically generate missions from components. For instance take the SA flight school and the waypoint missions. Why stop there? Generate some waypoints in random places and make the route different every go - now you can play it any number of times and it's always new. Say, assassination missions are simply a person, a place, and some story. Generate them.
Definitely more opportunities with what's available already; someone mentioned putting out forest fires with planes - great. Lots there - off the top of my head, crop dusting games, garbage collection, boat races, airlifts, helicopter rescue etc. Simply look at the resources and ask what's doable with them - I think that's cheaply done. Also when stuff is implemented for missions, like the SA magnetic helicopter or GTA3's bulletproof cars, keep it accessible afterwards at all times by default. You've got the reward so you shouldn't lose it, and there's more opportunity to use it.
Perhaps completing the game should reset everyone's hatred of you, or something similar - like God-style control over the environment. I found GTA3's constant gunfire after finishing it a little disappointing. In this respect I really liked GTA2's respect levels - a hidden/subtle version of this might be nice. Perhaps this is a good core for the gameplay, but I wouldn't expect to see it back.
For me the main thing would be some form of user-friendly (at some level, I don't mind some programming) scripting and customisation. Making mod development more accessible really extends the life of a game. It's highly unlikely to happen - dev tools now are licensed/proprietary, and more importantly it's time and effort spent for no money. Still, the best games offer this IMO.
What do you think? I've been playing GTA3 again so I've been thinking about this a lot. Wouldn't it be lovely if R* took notice?