A Visit to Barney Fife - S7-E18
Continuity mistake: While Andy and Barney are sitting on the porch, Barney's clip-on striped bow tie is clipped on the opposite way (stripes flip) when Ma and her family get back from "shopping." (00:14:45)
A Visit to Barney Fife - S7-E18
Other mistake: After Andy and Barney hear on the radio that another supermarket has been robbed they head over there, and in the shots at the supermarket note that many of the products on the shelves have their brand names covered with tape or scribbled over. For example, boxes of "Mrs. Cubbison's" stuffing/dressing and "Sunshine Cheez-It" are covered with tape. (00:16:40)
A Visit to Barney Fife - S7-E18
Visible crew/equipment: When Barney introduces Andy to Ma's boys, the actors' two tape marks are visible on the floor in front of the couch. (00:07:10)
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.