Updating slackware 13
You can let firefox to automatically update or update it manually from the about dialog. Are you aware that Slackware has updated packages in the /patches/ directory of a stable release?The most recent Firefox update was on 2 september for Slackware 14.1 for instance: that Slackware uses the Firefox ESR releases as updates for the stable releases.
I just unpack the new tarball into the version directory and have it "write into" and "overwrite" all. Just download the latest firefox x86_64 from mozilla site, unpack it in some dir in your home and make a soft link to ~/bin/firefox (add $HOME/bin to your $PATH).
Then, download the latest flash plugin from adobe site, untar it in /tmp (because it's packed to be untared on / so it spreads all its crap all over the sys) and copy only the to ~/.mozilla/plugins.