Package is in a very bad inconsistent state
and something about trying to reinstall it before removing it. However, it was an endless loop, and I tried several iterations of remove, reinstall, force remove, etc, but finally ran across the post I've linked to, and did the following to fix/remove it (I didn't try re-installing it, as I didn't need it):
sudo rm /var/lib/dpkg/info/flashplugin-nonfree.prerm
sudo dpkg --remove --force-remove-reinstreq flashplugin-nonfree
sudo dpkg --purge --force-remove-reinstreq flashplugin-nonfree
This finally fixed it, and made it so aptitude/apt/dpkg wouldn't complain while installing/upgrading other packages now, and only needed to run once, not multiple times like it did during some updates because of the above error.