The Taylors in Hollywood - S6-E8
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.
Revealing mistake: While Grandma Dynamite is on the roof sending smoke signals, Sonny is standing in the tree. When Sonny starts laughing we can see the bottom of his jagged clothing is now a mere straight line and his legs have vanished. (00:16:45)
Revealing mistake: In the shorts "In the Sweet Pie and Pie", and "Disorder in the Court", when there is stunt to be done that would hurt Curly, the stunt double is easily identified.