When the mayor first enters the sheriff's office, he has three pens in his breast pocket. By the final shot, he has only two, without ever removing one.
The chauffeur told Barney that the limousine was registered to the governor. The governor's car would normally be owned by, and registered to, the state and not the man himself.
In the opening scene, Barney is walking along the sidewalk when Chester throws his gum wrapper on the street. After scolding the group, Barney changes his direction and walks back in the direction from which he just came.
The license plate on the governor's car reads "DRLVE SAFTDEYE" instead of "DRIVE SAFELY" at the top and "NOTH CAPOLNIA" instead of "NORTH CAROLINA" at the bottom.
Andy thanks the governor for "coming down" to see them. As most TAGS fans know, Mayberry is a takeoff of Andy Griffith's hometown of Mt. Airy, which is northwest of Raleigh, the capital of North Carolina.