I too experience this bug and am able to reproduce it 100% of the time with every Firefox version (0.9 through 1.0.4):
1) Visit CNN.com
2) Have CCleaner clear Firefox cache
3) Reload page
You'll notice the CSS stylings have been lost and page reloads won't restore them. Only closing out the browser will reset things to normal. I've also experienced entire websites no longer loading after performing a clean with CCleaner while Firefox is open.
The advise of closing the browser before cleaning, while valid, is inconvenient.
admin, you may want to look in to the X 0.6.3 cache cl