Dick Is From Mars, Sally Is From Venus - S1-E4
Continuity mistake: In this episode Dick decides that Tommy has to go to school, but in 1-2 "Post Nasal Dick" Tommy already goes to school.
Suggested correction: That's just because these episodes were aired out of order of their production. "Dick Is From Mars, Sally Is From Venus" was the 2nd episode produced (production code 102) while "Post Nasal Dick" was the 5th episode produced (production code 105).
Continuity mistake: In the scene where Harry and Tommy are sitting in the living room, Sally comes by with a drink for Tommy and the shot changes when she is behind Harry and walking towards Tommy. But in that next shot, Tommy is already holding the drink.
Continuity mistake: When Ms. Dubcek is showing the Solomons the attic apartment in the pilot episode, they enter (and she later exits) through what is Dick's bedroom in all subsequent episodes. Additionally the staircase at the back of the living room that serves as an entry point is completely missing.
Continuity mistake: As Harry is leaving the party he is dry despite having just been in the shower fully clothed.
Continuity mistake: The dog that Harry brings home suddenly has a collar after Dick sets him down on the table. (00:02:40)
Continuity mistake: When the dog is on the table, the book on the right of the table changes position between shots without anyone touching it.
Continuity mistake: When Nina asks when Dick's birthday, is the papers on the back of her clipboard change position between shots.
Continuity mistake: Mrs. Dubcek says that she doesn't allow dogs because she is allergic to dogs, but in a later episode she claims that she doesn't allow dogs because she has 6 cats buried in the back yard.