I would like some sort of an extension to the contests. They were enjoyable and all, but they were just too damn ephemeral. As soon as you beat all five categories, there was nothing to do afterwards. :<
Ideally, I would like to see your Pokemon be able to go onto nationals, where you get to compete with winners from across the known nation in a tournament-style setting. No, I am certainly not advocating travel to older regions within the game itself, merely the integration of the contest winners from these places in a giant contest hall somewhere in the new region. Of course, your character would represent the new region, and when you win the thing, you would get some awesome prize like a Master Ball or a Lucky Egg (don't worry, it would be a doozy so by no means is this a giveaway). However, once your Pokemon wins in the nationals, you cannot enter that Pokemon or any evolutionarily-related Pokemon into nationals and still be eligible for this prize.
In addition, I would like to see this be integrated with the online/WiFi capabilities about which Nintendo seems to be raving. With this, people from all over the world would be able to enter their Pokemon that have championed the nationals category in their games, and the prizes would be something phenomenal like a ticket to get a rare Pokemon or something. Through the contests and the WiFi capabilities of the DS, geographic locations of players would no longer be as great a factor in obtaining tickets for those ultra-rare Pokemon.