It sounds like you aren't using the latest release of Moodle (1.0.1) ... what you are describing is a known problem with 1.0 on a few servers that I fixed in 1.0.1 (and the fix is controlled by the $CFG->slasharguments variable).
I doubt it could be Mozilla (it's my main browser too) unless you had cookies disabled for that site, but I'm glad the problem has resolved itself. Very strange. Perhaps it is a caching thing.