Goober Goes to an Auto Show - S8-E22
Factual error: Goober and the Taylors stop and get gas in Raleigh before heading back to Mayberry. As they are waiting, a Coors Brewing Company truck is seen driving past the service station. Coors Beer was not sold east of the Mississippi River until the mid-1980s.
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.