When Dan Caldwell is able to steal Barney's gun and hold Andy at gunpoint, Barney is not wearing his badge in close-ups, but the badge reappears in the wide shots.
When Caldwell arrives at the Mayberry Jail, State Police are traveling Code 3, with lights and siren. The siren is heard prior to their arrival and the flashing light is seen during the exterior shot. Code 3 is used only in an emergency and isn't necessary when transporting an inmate.
When Barney and Gentleman Dan play gin, Barney deals only eight cards. In gin, the proper amount would be ten.
About halfway through the episode, Gentlemen Dan is in his cell and telling a story to Opie and Barney. The camera angles change from inside the cell, looking out, to outside the cell, looking in. A bit later, Aunt Bee comes in, the same angles are used again, then Andy comes in. These camera angles revealed one little flaw: when the camera is looking out from inside the cell, there is the key ring in the door. When looking from the outside in, the key ring is nowhere to be found.
When Dan finishes his story about Baby Face Nelson, the shot of Opie sitting up is played in reverse.
The calendar in Dan's cell shows a month thirty days long with the 1st on a Sunday. This doesn't match any month in 1961. Going backwards or forwards, it would be either November, 1959 or April, 1962.