No "do you want to battle" messages. One of the things that got on my nerves was getting ready to fight my Rival or the bad guy, and them asking me if I want to battle instead of forcing it. I liked the unexpectedness of being able to be thrown into a battle at any moment from past games.
Relevant "Rivals". Shauna and Calem/Serena are the only ones really relevant. The other two didn't do anything even remotely meaningful or cool, they were just there.
More Aggressive Rivals. One of the things I liked about early games is the actual antagonist aspect of a Rival. You get fired up after you beat your rival and he tells you that you suck anyway, it's not as fun when they're like "Oh, your so much better than me". My Ideal rival system would be three or four that are serious about battling, but go about it in different ways, so you have (for example) the Jerk trainer, the surprisingly strong trainer who emphasizes on pretty pokemon, the strongest one who is kind to their Pokemon (Champion?). I'd also like to see one of these Rivals join the evil Team of that game.
More Post-Game exploration. There was only Kiloude town and... that's all? Nothing else in the region was really locked off before you beat the elite 4 (save a restaurant, Looker stuff, the last room of a cave and the one-room Mewtwo cave).
Event Pokemon. This is something I've always wanted, but I want to go to a town and have someone tell me there's a Pancham destroying stuff throwing a tantrum and I have to go calm it down (which I can then catch). Things like that to make me feel more connected to the world and immersed in it. It's happened once or twice before, but I'd like to see at least two in a game.