I really hope we get side quests. It makes the games much more fun and immersive. I'd hope to have some sidequests where you have to explore a castle that's I don't know, haunted by ghosts or something? Could be really fun, I think. I'd also love some mini-game/side quests where you could do quests with people over wifi, whether it be a random person or friends.
As for more contest ideas, I'd love to see contests again, but expanded into how they are in the anime! That'd be amazing, fun, and wasn't really possible before with sprites, but is now, due to 3D models being able to perform more motions more easily than sprites. I'd also like something similar to the capture the flag game in D/P/Pt (which I never played, but it seems fun) except over wifi once again, as having someone to play infrared with isn't always possible.