HM's. Or at the very least relegate them to a "fifth" slot that you only use in the field and doesn't take up your four battle move-slots (unless you want to use the HM move in battle).
Events. I'm happy that I can get them now, but I'd rather have rare legendary Pokemon (like Victini) and other stuff in the game after a certain point, not via event. I just now was able to get Wi-Fi, and said Wi-Fi is McDonalds.
HMs also need to go. They're just really annoying.
If you don't live in JP or USA use Wi-Fi.
No Wi-Fi? It's the 21st century, get it. There are many alternatives for Wi-Fi.
Video games are meant to SELL, not pirate off the computer, it's illegal.
If you're playing on an emulator, too bad. It's your fault for being cheap.
ANYWHO.
What would I like to change?..
I'd want to add the Pokeradar. It's harder to find shinies now.. :|
The following Pokémon feature is already gone in Gen 5, so there's no need to mention that.
I'm going to go further than the event haters and say version-exclusive Pokémon (and all other stupidly difficult to obtain Pokémon, which incidentally includes events). You can make all the claims you want about it promoting trading and social interaction (no longer true with wi-fi); the only reason there are version exclusives is to sell more games. It's a very simple and successful marketing strategy, but it's terrible as a game. I don't like having one game for the price of two (or even up to 5, across multiple platforms if you want to catch 'em all).