I can think of a ton of things actually.
-Expand on the field abilities system that allows you to use your own Pokemon instead of just rentals or wild Pokemon (although if you don't have a suitable Pokemon, you can still use a rental ability). In later generations, you could also clear different obstacles in multiple ways. You could cut down, ram, or burn a tree, cross a river by surfing across, jumping across, using a vine or web to grapple across, or creating an ice bridge.
-Add a trainer class system where you can select a certain trainer class for both in-battle out-of-battle perks. For example, you could choose to be a Swimmer which would increase your Pokemon's Speed in the rain in battle and increase Surf speed out of battle.
-Expand Pokedex functionality so it's actually, you know, a useful resource instead of just a list of Pokemon with lore blurbs and location data. Including move data, evolution data, breeding data, etc. (if necessary, they could have it fill in as needed to prevent spoilers) would make it a REAL Pokemon encyclopedia instead of just a joke of a device that you'll barely ever use. Serebii would probably hate this idea (less reason to come to the site) but it would be a tremendous improvement for the games.
-AI based NPCs that you can dynamically talk with instead of having scripted responses. Instead of your character being a blank slate that never speaks a word, you could supply your own dialogue with a microphone and the NPCs would react to it (this one probably wouldn't happen anytime soon, but I think the technology is there or at least pretty close).
And that's not even getting into all of the features they've left behind from past games that should be brought back, like Contests, Secret Bases, Battle Frontier, Join Avenue, Friend Safari, Dexnav, etc.