Opie Steps Up in Class - S8-E5
Continuity mistake: When Aunt Bee picks up Opie at Billy's house, she parks the car in front and walks up to the front door. In the wideshot there's a space of approximately 3-4 feet between the blue window shutter and the door trim under the pediment, but in Aunt Bee's closeup there is no space whatsoever.
Opie Steps Up in Class - S8-E5
Continuity mistake: When Aunt Bee drives up to the Hollander house with Opie, in the wideshot the car's rearview mirror is affixed to the windshield, but in the closeup the mirror has vanished.
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.