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.
Daddy's Little Beauty - S4-E12
Continuity mistake: When Fred is trying to work out what kind of talent Pebbles has, she has her bathing suit on. When Pebbles is seen crawling onto the stage when it's her turn, she has her regular clothes on, and when Pebbles is on the stage with Dino, she has her bathing suit on again.