Pretty much what the title says. You can't access the store to either add games to play later, to your wish list or to your cart. You can't track gamerscore, you can't claim games with gold. You have to upload captures to xbox live before they show up on the app. These are just a few missing things I can think of.
Edit: Thanks for the awards you guys. I'm just glad, most of you share similar sentiments. Hopefully Microsoft and Xbox make some changes soon.