Continuity mistake: The father was known as Clifford in the beginning but the name was changed to Heathcliff (you can see this on the nameplate for his office).
Continuity mistake: After Theo gives up an extra $100 for clothes, he is holding $300 left in his hand. However when the camera switches back to Cliff, who asks how much is left, it switches back to Theo, who is only holding $200 left.
Mr. Fish (a.k.a. Goodbye, Mr. Fish) - S1-E2
Continuity mistake: While some of the family is eating, the cup in front of Denise disappears than reappears.
Mr. Fish (a.k.a. Goodbye, Mr. Fish) - S1-E2
Continuity mistake: During the scene when Cliff is explaining to Rudy that her fish is dead, the fish food disappears at one point then reappears.
Breaking With Tradition - S1-E6
Continuity mistake: Theo and Cliff walk into the kitchen and Cliff sets the basketball on the counter. Theo walks upstairs. When the camera is back on the counter the basketball is gone.
Rudy's Sick - S1-E12
Continuity mistake: When Rudy is lying in her bed when Cliff is telling her about the germs in her body, her position on the bed changes between shots.
Continuity mistake: When Cliff is giving the kids their dinner, the pan cover keeps changing position.
Continuity mistake: The amount of water in Clair's cup changes a couple of times, most noticeably after Cliff tells her what she is eating, she takes a drink and the cup is about 1/3 full. She gets up to go find Theo, and now there is very little water in the glass.
Continuity mistake: After Cliff talks to Peter, Theo is told to run to the neighbors across the street. However, he can be seen in the background of some shots when the twins do their game. As soon as the twins finish, Theo is shown coming back into the house.
Continuity mistake: At the very end of the episode Clair's glass is suddenly fuller after Denise gets done singing.
Continuity mistake: Cliff says "a young trumpet player while sitting in the bandstand watching the dancers". But in all the later episodes, Russell plays the trombone, and he had been for a long time.
Continuity mistake: The amount of milk in Robert's glass changes a few times throughout the scene in the kitchen.
The Dentist - S2-E16
Continuity mistake: The amount of orange juice in Cliff's cup changes - you see him filling his cup, the next shot it is almost empty, a couple of shots later it is now full again.
Continuity mistake: When Theo puts the phone down, the handset cord is next to the phone. The next shot it is now under the phone, when the phone rings it is now next to the phone again.
Continuity mistake: In this episode, Rudy is riding her bike around the house which is right on the corner of a block. Since when is their house on the corner?
Continuity mistake: After Clair turns off the record, the folder on the table changes position.
Continuity mistake: When Rudy comes down the stairs and wants a lemon, Cliff is cutting one. In one shot it is fully cut. He givers her a piece of one he had cut earlier. When Rudy leaves suddenly he has a uncut lemon in front of him that he cuts.
Continuity mistake: Cliff takes the empty orange juice carton out of the fridge and puts it on the stove. When Theo comes in it is now on the counter next to the stove.
Continuity mistake: When Vanessa walks down the steps and drops all her papers, they are shown on the steps, then off the steps and then on again.
War Stories - S3-E11
Continuity mistake: Towards the end of the episode, Cliff Huxtable is sitting in the living room with his father Russell, Sgt. Stokes, and Homer. He is telling them of an incident that happened while he was in Bermuda. He is using dominoes to explain his story. At first there are about six or seven dominoes standing up on their sides. The camera angle switches, and all the dominoes are flat on the table. It goes on for a minute or so with the dominoes lying flat on the table. Then when Russell, Sgt. Stokes, and Homer get up to go for a walk, the dominoes are standing up again.
Chosen answer: That is the song "Open the Door Richard."