I found that both my
~/.mozilla directory trees were owned by
root:root and should have owned by username:group. This was coming off a fresh install of 12.04 LTS therefore I suspect a bug in a setup script.
Make sure you are in your home directory and your own userid:
sudo chown -R YourUsername:YourGroupname ./.mozilla
sudo chown -R YourUsername:YourGroupname ./.cache/mozilla
Replace YourUsername with your own username, and YourGroupname with your preferred group which by default is the same name as your username.
The .mozilla directory was easy to find, however the .cache directory was not obvious to me. I was able find firefox was looking at the .cache directory by starting firefox and leaving that error message dialog up, and while firefox was still running in a terminal entering:
lsof | grep firefox