Barney and the Governor - S3-E15
Visible crew/equipment: After Barney has given the governor's chauffeur a parking ticket and the chauffeur drives off, just as Barney starts to say that he's not wearing the uniform to win friends, we can see the reflection of the boom mic at the top left corner of the screen.
Barney and the Governor - S3-E15
Deliberate mistake: In the closeup of the license plate on the governor's car, the words over and under the plate number are deliberately taped to be unrecognizable. The original words are "drive safely" and "North Carolina."
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.