Audio problem: After the mayor tells Andy that his three daughters will be in The Beauty Contest, Andy phones Ellie and when she hangs up on him we hear Andy say, "Hello? Hello?" but we see him only mouthing the second hello.
The Statue - S7-E23
Audio problem: When Aunt Bee is introduced at the start of the ceremony, in the first wideshot as she begins her speech we hear her say, "Friends, neighbors, and fellow citizens of Mayberry" but it's not in sync with her mouth movements. (00:18:45)
Opie's Group - S8-E9
Audio problem: The band Opie is in has two guitar players but no bass player, even though you can hear a bass guitar being played.
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.