Carl Anthony Payne II (Cockroach) was fired from 'The Cosby Show' by Bill Cosby because he refused to get a haircut.
Nearly every sweater Bill Cosby wore on this show was sent to him by a fan.
Phylicia Rashad (Clarie) was actually pregnant during season 3. That's why she was absent for most of the season and when she was shown, she had something like a table or desk covering her stomach.
The episode entitled "Shakespeare" was originally scheduled to run in Season 3, but did not actually air until Season 4.