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: Near the end of the episode, all the castaways are passed out cold when Lord Beasley finally catches his butterfly. Right after saying the line "That's the trouble with you Americans - you simply don't know how to hold your tea" as he's exiting off camera, Mrs. Howell starts to open her eyes slightly, but then quickly shuts them again. Perhaps she thought the cameras stopped rolling.
Revealing mistake: When Rob is "playing" the piano none of the keys on the piano look to actually be pushed down. Also when he's scratching his back with each of his hands the notes on that same side of the piano are still played. He's not actually playing the piano. (Except for the last 2 notes or chords). (00:02:46 - 00:03:27)
Revealing mistake: Samuel Clemens (Mark Twain) spends a night in North Fork while the wheel of a stagecoach he is riding in is being repaired. Clemens is fishing at a lake and Mark McCain says, "You've caught a fish " Clemens tells the boy to reel in the fish. The boy jerks the rod and pulls the fish out of the water. The fish is obviously a fake which a stagehand had attached to the hook. The fish is motionless and is not even wet.