At the beginning of the Pilot episode, the Huxtables live in a different house and have four children, not five.
Jokes in the pilot, including the "Come here" bit and Claire speaking to no one in particular, were recycled from Bill Cosby: Himself (1983).
Cliff's full first name is Clifford in this episode, although his name is later Heathcliff.
Mr. T appears twice in Theo's bedroom: once in a poster near the door featuring a headshot and once in a movie poster for Rocky III (1982) on the far wall.
The episode won an Emmy Award for Outstanding Writing in a Comedy Series.