Dawson Casting: With Sondra, who was supposed to be in her early twenties. Sabrina LeBeauf, who played her, almost didn't get the role because she was only 10 years younger than Phylicia Rashad.
Averted by most of the other kids. When the show started, Lisa Bonet (Denise) was 17, Malcolm-Jamal Warner (Theo) was 14, Tempestt Bledsoe (Vanessa) was 11, Keshia Knight Pulliam (Rudy) was 6 and later addition Raven-Symoné (Olivia) was 3; everyone's actual age was also their age on the show. Erika Alexander (Pam), on the other hand, was 21; Pam was supposed to be 16.
Hey, It's That Guy!: Adam Sandler as one of Theo's high school buddies, Angela Bassett and Iman as patients of Cliff, Naomi Campbell as the girlfriend of one of Theo's friends, etc.
A pre-Star Trek: The Next Generation, Gates McFadden guest starred in an episode. More specifically, she's one of the party guests in the 3rd season episode that celebrates Cliff's 50th birthday.
Throw It In: Bill often kept the camera rolling when his many child co-stars would make mistakes because he felt it was funnier that way. In general, there was a lot of ad-libbing that made it into the final cut of each episode. Examples include:
Rudy's friend Peter was never supposed to be silent. The child actor froze once he was on camera and Bill took the opportunity to turn the character into the Silent Bob.
Then there was the episode where he was taking care of Sondra and Elvin's twins. They would continually look up at the obvious stage lights. Bill played off on it as if the babies kept staring into space. One of the babies spit-up in the very same episode but Bill cleaned the baby up and kept going.
One episode was to just show Cliff making a meal, and Cosby turned it into an extended bit lampooning Julia Child.
Early seasons had Rudy forgetting her lines, so Bill Cosby just spoke them for her and kept going.
One actor continually rendered "Doctor Huxtable" as "Dostor Husstable". It simply became a trait of his character.