Ernest T. Bass Joins the Army - S4-E3
Revealing mistake: When Barney picks Andy up and they get back to the courthouse, they find Ernest T out of the jail cell again and breaking more windows, and in the shot of Ernest T leaping in the air we see it's actually a flipped shot - note the backwards "snack bar" in the window (that store is later when Ernest T tries to break the new glass for the courthouse).
Aunt Bee the Crusader - S4-E15
Revealing mistake: Toward the end of the show the rooster, Bo, is drunk. If you look closely you can see the two strings pulling the rooster's neck sideways.
My Fair Ernest T. Bass - S4-E17
Revealing mistake: At the start, when Ernest T. throws the rock at Mrs. Wiley's window and it breaks, the area around the hole flutters in the breeze - it's obviously not a glass window used for the stunt.
Revealing mistake: Barney and Mr Weaver scuffle in the dark. When Andy enters the store he turns on the light, but the light switch is still in the off position.
Revealing mistake: When Andy, Barney, Gomer, and the kids are at the campsite in the woods, during the daytime scenes the only shadows that should be seen are the ones being cast by the sun, but there are shadows being cast in different directions due to the set lighting.
Answer: In S3 x E11 Convicts-at-Large, there is a character named Big Maude Tyler, who is the leader of three female escaped convicts. Andy listens to the radio as the news announcer says that Big Maude's aliases include Clarice or Annabelle Tyler and also one amusingly named Ralph Henderson.
Super Grover ★