Other mistake: At the beginning of the series, Hope Summers' character is called Bertha Edwards. Later in the series she is Clara Johnson; still later she is Clara Edwards.
Other mistake: When Ralph Mason walks into Walker's Drugstore and asks to purchase a tin of pipe tobacco, the tobacco tin that Ellie puts on the counter has black tape across the top covering its brand name, which is "Tuxedo."
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.