Opie's Group - S8-E9
Visible crew/equipment: After Aunt Bee asks Clara to speak to Opie, in the interior shot just as Clara walks into the house we can see the two tape marks on the floor, where Clara and Opie will stand.
Opie's Group - S8-E9
Visible crew/equipment: After Opie leaves Emmett's shop it cuts to the Taylor dining room as Opie is walking away from the server with salt/pepper shakers, and when he sits down we can see the actor's tape mark on the floor by the server. (00:06:25)
Opie's Group - S8-E9
Visible crew/equipment: While Opie and his band are playing at the party there are shots of the kids dancing, and in the shot of a girl with blonde hair wearing a blue dress, the camera angle is low and we can see the top of the set. (00:10:25)
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.