Sorry about not posting software specifics in my first post, I use LMDE with all updates (level 1 through 5) installed via MintUpdate, which means I currently use Firefox 3.6.13.
Before creating this thread I had tried uninstalling mint-flashplugin and installing flashplugin-nonfree instead, as well as marking firefox for reinstall in synaptic, both without success. However, I tried lmintnewb's suggestion of uninstalling firefox completely and then installing it again, and that worked.
I will try secipolla's idea if it happens again. It seems a bit simpler and less intrusive, assuming it works.
Thanks for your help everybody!