Visible crew/equipment: After Andy gets the phone call about Sam's victory, when Sam is pushed to give a speech, a few white tape marks are visible on the floor near the fireplace.
Visible crew/equipment: After Emmett talks to to the diner owner about having the bus stop moved to double his diner business, when Emmett walks down the block, the reflection of the moving camera dolly is visible in the store window.
Visible crew/equipment: When Andy, Howard, and Goober walk into Emmett's shop to tell him that Sam's running for head of City Council, the shadow of the boom mic is moving on the wall behind them, at the top of the screen.
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.