Chromium-browser always reports it didn't shut down properly when I first start it after a shutdown/reboot.
I guess I could close it manually first before shutting down, but other apps seem to be ok with stopping themselves as the system shuts down, so why is chromium having a problem (and can it be fixed)?
If the problem persists try removing
rm -r ~/.config/chromium/
There's been a few updates for 12.04 and the problem seems to have gone away. Maybe they fixed something.