Also, I like how you can see how an item affects your character in-game (damage, health, protection). I would like to see this kindness while browsing the auction house as well.
I think it was a great change to save search options when switching from the ah to the rmah. However, I would like to see your searches saved when exiting the auction house. Perhaps allow players to save their searches with specific parameters so they do not have to type them in every time they search the ah or rmah.
An in-game auction house would be nice so I could post items on the fly.
I'd like to have timers on auctions show down to the second how much time is left.
Perhaps implement some sort of trading system comparable to steam in which players can trade items for games. I think that'd be pretty neat to be able to trade in-game items or currency for actual copies of blizzard games to their fellow players.
A mail system might be kind of cool.
That's about all I can think of at the moment. I'll try to post more as the thoughts gradually come to me. Please post your ideas for such changes and feedback to the latest version of the auction house as well fellow forum-goers if you feel inclined.