I answered this earlier, but still had a few other ideas. Originally, I posted
-more overworld moves. The HMs always intrigued me, but it would be cool to have something like Rain Dance make it rain in the game and trigger different events.
-Have a physical version of hidden power.
-Have partner pokemon like in HG/SS, but be able to control them separately at times and use them to solve puzzles with the trainer. (Think Legend of Zelda 4 swords)
-Have it where gym leaders aren't limited to the pokemon around the area. For instance, in Heart Gold, how Morty has the Gastly evolutions for his gym. I know his rematch team covers this, but it feels kind of boring for them to just have the pokemon around the area. It would make sense that he's traveled around the area and is able to obtain other ghost types, so it would be a bit more interesting. Then once the rematch comes, he can have the new pokemon as well as his evolved originals.
-Give moves, abilities, etc. To power up some deserving pokemon. Flareon knows exactly what I'm talking about.
-Have a better move for entry hazards than just rapid spin. I don't mind the entry hazards, and they can be stopped with a taunt or something like that, but sometimes, you might want to use rapid spin to do away with them, especially if you have something weak to it. While rapid spin does the job, it's kind of frustrating having such a weak move just to deal with that. It would be nice to have a stronger move for that.
-Raise the base power of feint. If it was stronger, it could be a useful move competitively to break through those annoying stallers.
-Adding on to the overworld moves, things like using rain to trigger events like raising water in a dried up river, or sunny day to melt a giant glacier, and other things like that. You wouldn't even have to use the weather moves. There are several other ideas out there.
-they've done this before, but the cross generation characters are a pretty awsome feature. For example, Looker and Cynthia appearing in B/W. there are some other characters that would like the updated teams, as well as serving some use in the plot. Elite 4 Karen is one that comes to mind.