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.
Plot hole: Live 50th anniversary episode, aired December 9th 2010 - When Sally is allowed into the rubble to comfort Molly as the firemen attempt to free her, one of them says they'll get Sally a hard hat. When we see her talking to Molly in the rubble, she has no hard hat on and instead one of the firemen is hilariously holding his hand above her head.
Like This It Means Father... Like This - Bitter... Like This - Tiger... - S4-E15
Continuity mistake: The bruise on Wilcox's cheek switches from the right side of his face to the left and back again several times throughout the episode.
Continuity mistake: The packages Drake and Kathy place on the table beside their coats have disappeared when they return for the coats a few shots later. (00:19:00 - 00:21:20)
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.
Continuity mistake: In all other episodes of this season, Officer Dan has blonde hair. This one episode, Officer Dan has gray hair and his face looks completely different from other episodes.