Like most programs nowdays, firefox updates are designed for either RedHat/Fedora or a Debian/debianish such as Ubuntu. Slackware and Vector use a different directory structure and a different package format. Updates should always be done with a package tool such as GSlapt, or by hand if you want something very in particular.
Firefox updates are in the testing repo. In GSlapt, enable the testing repo ( edit - preferences - sources ) and install. Firefox, Pidgin, and e-mail clients are usually security-related updates and should, IMO, be installed soon after they're available. You may want to wait for a couple of favorable replies to the forum announcement of the package before installing. I suggest turning the testing repo back off after getting exactly what you came for.
Firefox updates are packaged for Vector very quickly, but not as soon as the upgrade request appears in firefox itself. If ff suggests upgrading, just look for the New Package forum post; it'll be soon. Firefox 3.6.10 is available. When started, it will suggest flash upgrade. A good tutorial for that is here