Figure out the whole "state" thing

[matthewturk]

There's a lot of state that we ... just don't deal with in this extension. File browser tabs that should probably go away when the widget gets disposed, for one thing! And for another, the widget tabs themselves shouldn't re-create unless we're sure the state is correct.

Seems like a good opportunity to learn what the various "dispose" methods do, and figure out how to handle them.