Continuity mistake: Aunt Bee and Captain Wolford are sitting on the porch. The Captain extends his left arm behind Bee's head and rests his hand on her shoulder. In the close-up of Bee, there is no hand on her shoulder. In the following shot, the Captain's left hand is in his lap.
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.
Revealing mistake: A shot shows the interior of the church where Andy Taylor and Helen Crump will be wed. Shrubs and trees are visible outside the church entrance but they are obviously just a painted backdrop. As people enter the church, they cast shadows on the backdrop.
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.