When Thelma Lou and Helen confront Andy and Barney in the sheriff's office with the "Fun Girls," the lipstick on Barney's right cheek disappears briefly and reappears again.
When Otis comes into the courthouse, Barney can be seen sleeping on a couch in the back room, in other story lines there is a bed in the back room.
At about the three minute mark as the "Fun Girls" go speeding by Andy says they were going 50 mph. One minute later after Andy pulls them over he says they were going 45 mph.
When Andy and Barney are chasing the Fun Girls to stop their speeding through town, they turn a corner just as the girls pull over. The street they stop them on clearly shows a set of street car tracks in the middle of the road, a public works feature that would not have existed in a small town such as Mayberry.
The state of North Carolina stopped using front license plates in 1951. However the Mayberry patrol car is still displaying a front license plate JL-327 in 1965.