Is there a way to add Boards and other features in the mobile app?
No, the current version (1.3) of the Trello iPhone app does not allow adding of Boards.
However, I did see a tweet sometime in the last couple of days from someone saying they were really excited about what's going to be in the next version. Unfortunately, it didn't give any specific info, and I can't find it right now.
18 Jan 2012: Version 1.4 doesn't support adding boards either, though it does have some other nice improvements.