The Return of Barney Fife - S6-E17
Continuity mistake: At the reunion you see a sign that says class of '48. In season 3 They had a reunion and it said class of '45.
The Return of Barney Fife - S6-E17
Continuity mistake: When Barney and Andy are at the Class Reunion dinner, there is a band playing, but the accordionist's fingers aren't in sync to the music.
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.