You dont have to install firefox directly from mozilla site, the software would be available in the mint repositories. Try searching for firefox 3 in mint install. If not, start synaptic & search for firefox 3, you should be able to find it there. In the worst case, you can use the .bz2 file you downloaded. Instead of douvle clicking on it, right click & see if you have any options to install the .bz2 file (each distro has its own package format & .bz2 is used by slackware).
Don't fix it if it ain't broken, don't break it if you can't fix it -Husse