I am running a fresh install of Mint 13, with Firefox 20, all is good.
This machine has jumped ship from Ubuntu 12.04 with MATE desktop because
last week an update knocked out the icons on the app panel. The .mozilla
folder was reintroduced to Mint from the prior Ubuntu system, no
problems (except for the usual stupidity of Flash no longer being
supported, etc).
May I suggest:
Backup (export) your bookmarks
Record which plugins you have installed, also record anything you
can't do without such as saved passwords etc.
Rename your .mozilla folder
Create an empty .mozilla folder with same profile.ini and
<random>.default folder (this should help with migrating back to the
original one in small steps)
Progressively introduce plugins and settings from the old .mozilla
Good luck
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