Those runtime errors with IE make me think the problem is more basic to your system than FFox. So I agree that a good scan for spyware/malware and viruses is probably called for.
Meanwhile, I'm using Firefox 1.0.6 here, as well.
Try pressing f7 and switching it out of "caret browsing" or in if it's already out. Sometimes, on mine, this will kick in unexpectedly and mess with the focus. Come to think of it, I haven't had this happen for the last couple of versions, so upgrading may do it for you if this is the problem.
Do you run any themes or extensions? Try starting FFox in its safe mode (note, not Windows safe mode, but FFox's safe mode - assuming you're running under Windows, it will be under Start > All Programs > Mozilla Firefox) - this disables all themes and extension to see if that is the source of your problem.
Mozilla has an excellent user-to-user bbs at
http://forums.mozillazine.org/index.php, you're probably better off taking your problem there. Be sure to mention operating system, FFox version, and as complete a description of your symptoms as possible.