While Andy and Barney are waiting outside Sheldon Davis' hotel room door, the room number is shown to be #81. The Mayberry Hotel is a small, three-story building. This means that each floor would have approximately 30 rooms.
Sheldon Davis (Jay Novello) shakes hands with Andy, Floyd and other townspeople to steal their watches. However, when Andy asks for the time, two of them look at their left wrists when they had clearly shaken with their right hands.
As Sheldon Davis enters Mayberry, a "Welcome to Mayberry" sign is on the left side of the road, not the right.