Honestly the current battle system is outdated and needs to be overhauled. I mean, we've been using the static, single pokemon, turn-based system since the very beginning. At least double and triple battles are a little more interesting imo, but they primarily use single battles for just about everything, which are an artifact of the past. What I think they should do is implement the battle system from Mystery Dungeon into the main series. Except just restrict everything to a small area for each battle, and the terrain varies depending on where you are, with partial random generation. Not only does that system allow for much more interesting strategies, since you can move around and use cover, plus some pokemon can't go on certain terrain, like you need to be water type to go on water, unless you have levitate or flying type. Moves have more AoE depending on the move itself and can be aimed. Not to mention that there are no real limitations on the size of the battle. You can do 1v1, or you can do 4v4, or even 6v6. When the bad guys fight you it could start out 1v1, but then 2 other guys run up mid battle and throw out 2 more pokemon.
Some additions to the system that could be added would be things like I said earlier about the terrain being small, but based around where you were, with some random parts, like if you're in the ocean there would probably be a few small islands so that your non-water and flying types have at least something to not die, but of course that doesn't mean you're not screwed if you get only a small island to maneuver while the other guy has the entire field. Another thing would be that when sending out pokemon, you could probably choose anywhere from your side of the field to drop them. Plus vision could be limited to what your pokemon could see maybe, on top of a straight view from your side of course, basically just the ability to not only move around, but also get out of your opponent's vision. Then moves like fly could reveal the entire map since you'd have a pokemon up in the air. Unless of course of there were also tunnels.
Other than that overhaul, I'd like to see a story about more than collecting badges as its focus. I've always felt that the whole collecting badges things was more like a side-quest, with the reward being the whole pokemon league stuff and everything. Then the main game would be more about saving the world. Plus the non-badges related story tends to only take up a small portion of the game normally. I'd much rather it allude to something from the very beginning, like they kidnap your mom or something early on. Most of the trainer battles being from the bad guys directly trying to stop you, more than just random dudes at least. If random people battle you, the idea would hopefully be that they want to train so they can defend themselves from Team Rocket or whatever. Your rival would probably side with the bad guys, and that'd be why you'd fight him/her over and over again.
Oh, and bring back pokemon walking behind you while traveling, that was cute.