
Continuity mistake: When Andy finds the old newspaper clipping in Helen's box he tucks it into his pocket, but when he's looking at the clipping while he's at the office the newsprint on the back is entirely different. Then when Howard reads it the newsprint changes yet again.
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.