The main things that really annoy me is that pokemon are limited to 4 moves... and you can only carry 6... you should begin with a limit of say 3 and be able to upgrade the bag at specific points in the game up to a total of 8 ish... Also stats shouldn't be as limited. You should be able to keep a shinx and give it a stat boost item so that it has the stats of a luxio at lv15 and a luxray when it evolves again later on... 

I also hate the fact that shinys dont have any stat boosts anymore... I reckon they should have increased stats relying on the characteristic  of the pokemon. i know characteristic already slightly improves a stat but with shinies it should improve a stat alot more...