Revealing mistake: While Andy, Aunt Bee, and Opie are at the Hollywood studio watching a scene being filmed, when Andy mistakenly stands up and interrupts the filming we can see the wall and shelves behind the director, and it should look familiar because it's the wall and shelves from Floyd's shop in Mayberry.
Continuity mistake: Wilma opens the bedroom door to find Fred covered in flour, but in the next shot the bedroom door has vanished while Fred stands in the doorway.
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)
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.
Other mistake: In "Dunked In The Deep" (1949), Moe, Larry and Shemp go to a pier where a ship is docked. The picture of the ship has been flipped and the ship's name, SAN CAPEADOR, appears in reverse.