Barney shuts off the patrol car's emergency light after he stops Gomer for the illegal U-turn. When he goes back to the car after giving Gomer the ticket, the emergency light is back on.
Both Barney and Andy respond to the robbery with rifles. When they leave, Barney puts his rifle in the back seat but when Andy gets into the squad car, he doesn't have his rifle.
There are several inconsistent references in the series to Barney's tenure as a deputy. In this episode, Andy and Barney discuss how Barney has been a Deputy for 10 years. Next season, in Barney's Physical (1964), Barney makes a fuss about how Andy forgot his 5-year anniversary as a Deputy.
In the first scene, Andy and Barney are noting that Barney has served as Deputy for 10 years. They're viewing a 10-year-old document, dated August 10, 1953, authorizing Barney to be issued a gun as Deputy. Andy says something to the effect that he remembers it well and it was "10 years ago, last month". So this means that the "current" month is September, 1963. However, later in the day, Barney is in jail, crossing a date off a calendar in a month having 31 days, which cannot be September.
When Gomer is making his citizen's arrest of Barney, the townspeople standing behind him change positions as the camera angle changes.
Barney arrives at the filling station for the "emergency" call having extricated himself from his jail cell. But Otis left the key in the other cell door, on the other side of the room, where Barney could never have reached it.
Barney doesn't smoke and didn't have a chance to stop at a store before going to jail. So it's a mystery how he got a package of cigarettes, which he smokes in his cell.
In the final scene, Andy reads Barney's name as "Bernard P. Fife" from resignation letters in a file folder, whereas his name was "Bernard Milton Fife" in Class Reunion (1963) and his middle name was "Oliver" in A Plaque for Mayberry (1961).