In the pilot, Clair asks "Cliff, why do we have four children?" He replies, "Because we didn't want five." A few episodes later, Sondra was added to the cast as their fifth child, who was away at college.
When Cliff and Clair leave Theo alone in the house while they go on a ski trip, Cliff is carrying some skis out. He drops a ski and it knocks everything off Clair's desk. In the next scene, the objects are on the desk again.
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 no office staff, a single examine room, and apparently no waiting area.