Continuity mistake: When Andy and Barney catch up with the man who ran Fletch's truck off the road, the rearview mirror suddenly vanishes in the closeups that face the windshield on Bailey's car.
Visible crew/equipment: When Barney's reading the Sunday comic strip Andy comes in to close the jail in the courthouse, and when Otis walks out of his cell we can see the actor's chalk mark on the floor where he stands.
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.