When Andy and Barney are watching Sam plowing, there is heavy wind from the storm that's coming, but the trees in the background of the field are still and there is no dust from the plowing.
When Aunt Bee opens the door to let Barney in, the trees in the yard are not moving even though the wind is blowing.
When Sam and Barney were reminiscing about their wartime experiences, Sam recalled a company-sized patrol in Korea of about 200 men. A combat company consists of closer to 100 men.
Right after Barney tells Floyd that it's a civic order, Andy opens a door with a black mark on the bottom, but it's gone the next time they come through.