Continuity mistake: When Opie surprises Andy by telling him that he wants to take piano lessons with Clara, he heads to the piano to play what he already knows, and when Opie plays Chopsticks on the piano he's wearing a different shirt.
Other mistake: During the closing theme (early seasons), when Fred walks by to close the birdcage, Wilma is shown in the background sleeping and her entire mouth is missing.
Continuity mistake: "Rusty Romeos," a 1957 short co-starring Joe Besser, is a remake of "Corny Casanovas," a 1952 short co-starring Shemp Howard. In a scene using stock footage from the earlier film, Moe and Larry are fighting, and a framed photo of Shemp is on a small table next to the couch. In the following scene, using new footage, the photo is of Joe. (00:15:10)
Factual error: In "The State Vs. Chip Douglas", Ernie finds his missing 1914-D penny when it falls out of his pocket. A close-up shows an Indian head penny lying on the floor. The problem is that Indian head pennies were not minted after 1909.