Aunt Bee Learns to Drive - S6-E21
Continuity mistake: The car which Aunt Bee buys from Goober has a rearview mirror which repeatedly disappears and reappears between shots, throughout the episode.
Aunt Bee Learns to Drive - S6-E21
Other mistake: Aunt Bee says that Andy had to drive her to Clara's and Andy says it's not a bother, but Clara has always lived right next door.
Answer: It was a joke. They were supposed to be dumb hillbillies.
Both. According to later interviews with both Andy and the Dillards band (the real name of the band that played the parts of the Darling children, of which Charlene (Maggie Peterson - Mancuso was also a member) the reason the Darling boys never had any lines was because they would've had to have been paid if they spoke. In return for appearing without lines or pay, Andy promised to get as much of their music onto the show as possible which, he did. This obviously gave them a lot of exposure.