Well... there is a lot that I believe could be changed about the pokemon series. I'll say it right now though... alot of people have said they want it closer to the anime - the day they move in that direction is the day I stop playing pokemon, because I think that the combination of the anime and the art style picked up in gen 3 is what gave the series its kiddy image.
So to start, as mentioned, bring the old art style back, or get something better than the current one. The old one had attitude, and everything had a "badass" look to it. The new one... OMG ITS CUTE!!! If you were to compare the old art with the new art, you'll immediately see what I"m pointing out. While we're at art, why not a true 3D overworld? The battles should stay 2D, thats a necisity for any good pokemon game, but a full 3D world would be sweet.
The story needs to change for once. WHY does the main character want to be a trainer in the traditional sense, WHY does he want to challenge the Elite 4, etc. To mix things up, why dont we, oh, lets try making the player a runaway from home, and face the challenges of homelessness. Or, lets say you start the game as a member of an evil organization and the guilt drives you to attempt to destroy it from the inside. Those are just two examples, but they would be so refreshing after 4 games of repeated plots.
Make the evil organization actualy evil. Team Rocket went the closest to that with cutting off the slowpoke tails, now lets see an organization try to use weapons, inflict harm on actual people, do acts of terror - blow up the Silph co instead of just taking people hostage. Combing this point with the above, I'm saying we need a new, good story. Even if its loose, something different is needed.
Game play wise, there's not much that needs improvement. There are some, though. For example, make HM moves be items so we dont have to waste a move slot or carry an HM slave. Introduce some new types - gen 2 brought the Dark type, why aren't we getting any more? Change the level cap - 100 is a little low. NO FRIEND CODES, have random battles but disable the voice chat. You can do it with trades, so it cant be too hard for them to get battles going. Why not have the option to do 2 on 2 battles against only one trainer? For that matter, when trainers gang up on you, they both should be able to use 6 each, not be limited to 3.