Other mistake: While Sam is working in the yard, Goober drives up and hands Sam a registered letter from New York City. The post office had called Sam to tell him Goober was bringing the letter. However, a registered letter has to be signed for by the addressee. (The delivery receipt is form #3849.) Goober would not have been allowed to sign for it.
Other mistake: Sam Jones' son, Mike, tells Aunt Bee that the farmhouse has been in their family for 150 years. While showing Aunt Bee a photo album, he points to a photo and says, "That's my great-great-grandfather who started this farm." Pointing to a woman in the same photo, Mike says, "That's my great-grandmother. She lives in Philadelphia." It is very unlikely that the daughter of a man who had started a farm 150 years earlier would still be alive. Assuming the man started the farm when he was in his 20s, he would have had to father a child when he was in his 70s and she would now have to be in her 100s.