Other mistake: Floyd's car has the license plate number "RD 757" which has been seen on other vehicles in previous episodes.
Floyd, the Gay Deceiver - S3-E9
Other mistake: In the final scene near the end of the episode Floyd calls Andy "Andy Griffith". It's muffled, but if you listen closely it's audible.
Other mistake: When Barney is ready to pour the plaster cast into the shoe prints, there are only a few prints on the ground. There should be a continuous set of prints from the barn door to wherever.
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.