Game mechanics wise, get rid of those ridiculously high evolution levels. This game is just an insane grindfest, and killed a lot of my enthusiasm for playing :/ I'll probably end up adding a slight exp modifer cheat when I play to offset this, otherwise the tedium will drive me insane >.<
Futchimaru and Daikenki would be water/fighting, and Chaobuu and Enobuu would be fire/dark or just fire. The Gothiselle line would be dark/psychic.
Also, no more HMs, and instead have "field moves" or something that dosen't take up a move slot.
Graphics wise, my biggest thing would be choosing your appearance at the beginning, even just a few different pre-made designs would be a nice change. But what I would do is have customizable hair color, hair style, clothes, and face, with a shopping mall for new clothes and a hairstylist. (Face would be chosen at the beginning and unable to change)
Also the sprite choices for the previous gen monsters, some were good choices, but others should have had a better looking sprite from another game. Hypno for example, should have had his awesome HGSS sprite instead of that dumpy DP one. Others should have had DP or Platinum sprites instead of the HGSS ones. In cases where they were all bad, just make a new sprite
Someone suggested detailed backgrounds for battles, that would definitely be a nice touch as well.
The flying trio would look COMPLETELY different from each other instead of being clones.
Content wise, definitely add a battle frontier on par with Emerald, but this feature is probably being reserved for the 3rd game. The biggest change needs to be rematches, as others have said.
Other then those things, BW is pretty perfect to me!