Gesture-based movement would be very interesting. Using the app also got me to thinking about common interactions using links - i.e. click a monster's name to attack it, an item's name to pick it up, etc. That could take some doing, though - how could the client distinguish between an object vs. mob, for example.

Might be interesting to be able to hide room descriptions and tap to expand them somehow. I don't typically use them in-game anyways, and on the app it's even more in the way.