Goofs

In the first season, Cliff's name was Clifford. In later seasons, his name was Heathcliff. In the first episode of the final season, Clair calls him Heathclifford.

In the pilot, Clair asks, "Cliff, why do we have four children?" He replies, "Because we didn't want to have five." A few episodes later, Sondra was added to the cast as their their eldest-of-five, who was away at college.

A few times, Cliff has a nurse and or a secretary in his home office yet he handles all of the phone calls, makes appointments etc, without any explanation of why he has an assistant.

One of the records in Denise's room is Mr. Mister's "I Wear The Face" album. Several times in the the same episode, the record in her room changes from Mr. Mister's "I Wear The Face" to the Pointer Sister's "Break Out" to REO Speedwagon's "Good Trouble".

Often times throughout the series Theo's room and the bathroom use the same door. Also the the room directly across from Cliff and Claire's constantly changes from Theo's to Vanessa and Rudy's.

Cliff Huxtable is an OB/GYN in New York City who is successful enough to have his practice in the basement of his home. Yet he has a single examination room, no office staff, and (apparently) no waiting area.

It's established that Clair Huxtable was born in 1946 and that Sondra Huxtable was born in 1964 and Denise Huxtable was born in 1968. That means Clair was 18 when Sondra was born and 22 when Denise was. Yet it's also been established that Clair went away to Hillman College and married Cliff after her graduation while she was in law school. It would have been impossible for Clair to do those two things if Sondra was born in 1964 and Denise was born in 1968.