I think the very first thing that would be useful to work on for a mobile environment is making the reply editor design rock-solid.
Browsing around Discourse on a mobile device isn’t a good experience, but isn’t absolutely terrible either. The problem is when you try to reply to anything - the editor box jumps around the screen weirdly, and the toolbar is in the way so you can’t see anything. It’s pretty lousy on my Nexus 7 tablet, and I’ve had people tell me that it isn’t very solid on the iPad either, though that could be my custom theme also contributing.
Ironically I end up using my phone to reply when mobile instead of my tablet, because since @sam disabled the preview/toolbar on smartphones in the CSS, it is much easier to deal with.
The second thing that is very bad on mobile is the login screen, which is usually halfway off the display on my phone, and you can’t paste a password (bad for those of us who use LastPass).
I really think it would be a huge win.