I, too, dislike the fact that I can't remove phone numbers. If the people didn't call so often and if they weren't so annoying, it wouldn't be that bad, but they won't leave me alone! I'm not that far into the game (Goldenrod), but I'm already starting to get fed up with the number of phone calls (and I haven't gotten a single request for a rematch, so they've been pretty useless, as far as I'm concerned).
I also don't like the huge emphasis on the touch screen. It's fine for some things, but I wish I could easily navigate the PC and menus without using it. I feel like I have to go through an extra step or two to access things if I don't want to use the touch screen than I did in DPPt. I also don't like the stats screens for Pokemon. They just seem harder to read to me than the DPPt ones.
There are a bunch of small issues with the games (there are plenty that I haven't mentioned here), but overall, I really like the games, despite their issues.