I've now surfed with Firefox in Haiku, and it worked fairly well. I didn't manage to log in and post here though. The big issues seems to be the widget-code, especially which view has focus/mouse handling, getting drawing notifications from OS and the destructor code.
For instance if you move some part of browser offscreen and then back it will not redraw properly. Mouse seems to be locked to certain views, and it did crash on nsWindowBeOS destructor at least one time.
Not sure when I'll start really looking into those things though.