Visible crew/equipment: When Wilbur's in his car he thanks Andy and the rest of the men for all the shoe sales. As he drives off, the reflection of filming equipment is visible on the surface of the car, and when the car is offscreen multiple chalk marks are visible on the sidewalk, at the feet of the actors.
Visible crew/equipment: When the men have the misconception that Wilbur is a TV show talent scout, while they're at the barber shop talking about it, just as Floyd moves his legs to get up from the barber chair we can see the white T-mark at Jason's feet.
Visible crew/equipment: After Aunt Bee plants the seeds of suspicion in Andy's mind about the shoe salesman, when Andy and Barney cross the street the reflection of the moving boom mic is visible on their squad's windshield, just as Andy walks off to the hotel.
Visible crew/equipment: At the end when Aunt Bea enters the courthouse, she doesn't close the door completely. You can see a hand from outside grab the door, and close it very slowly. (00:23:20)
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.