Has anyone ever noticed that the plaque on the Huxtables' front door that said Clifford Huxtable, M.D. stayed up there for the entire series? I just now picked up on this. I guess it was never fixed even after it was established that Cliff's name was Heathcliff.

I think it only said Clifford Huxtable in the pilot episode and maybe a few early Season 1 episodes because it was later changed to Heathcliff Huxtable.

Nope, it was never changed. If you watch the season 6 episode "Cliff and Jake" you will notice it in one of the outdoor shots of the Huxtable house. It's a little blurry but it says Clifford Huxtable, M.D.

The whole first season was full of strange contradictions: the plaque that had the wrong name, the weird living room that led into the dining room, the fact that Cliff and Clair only had four children...