At 13:38, when Aunt Bee blows the lock of hair off her forehead, the camera changes. In close-up, she holds the dinner plates in her left arm but in the two-shot, she hugs the dinner plates with both arms.
At 2:26, the courthouse scene cuts to another camera when Aunt Bee says "terrible blow". Her right hand is suddenly at her nose, wiping, where it was not before. Returning from a three-shot back to a close-up, her hand is suddenly back down on her lap as if it was always there.
Near the end of the episode, when Andy psychs out Barney about his health, they are playing checkers. At one point, Andy moves twice without Barney making a move in between.
The calendar in the main jail cell shows a month with thirty days, with the thirtieth falling on a Saturday. In 1963, that would set the time of this story in November. The side cell bears a calendar also with a month of thirty days, but with the thirtieth falling on a Monday. In 1963, that would set the time of this story in September. The episode originally aired in March of '63.
When Colonel Harvey does his smoke signal trick, the tip of a black hose is visible in his left hand.
Aunt Bee chides Andy for not letting her know Barney was coming to dinner, as, with a guest already coming, she only set the table for four. Later, after it's established that Barney isn't staying, she sets the table for four. Her character may have only thought she had set the table or misspoke that she planned on serving only for four (a potential clue to her drunkenness), but the fact that the table wasn't set isn't brought out in the dialogue or by camera work.