In the opening courthouse scene Andy, Barney, and Opie are gathered behind the desk talking. The flagpole changes positions between shots of Barney and shots of the group. In group shots of the three, the flag is partially covering the left frame of the map behind Andy's desk. In Barney's closeups, the flag and pole are about a foot to the left of the map.
When Aunt Bee comes into the living room, she's holding the bottom of the coffee pot with her bare hand. It would've been hot.