Continuity mistake: In the closeup of Barney's yearbook picture his name is listed as "Bernard Milton Fife," and Andy even reads it aloud, but in the previous episode from season 1, "A Plaque for Mayberry" Andy says that Barney's middle name is Oliver.
The Andy Griffith Show (1960)
1 continuity mistake in Class Reunion - chronological order
Starring: Ron Howard, Don Knotts, Andy Griffith, Frances Bavier
The Taylors in Hollywood - S6-E8
Revealing mistake: While Andy, Aunt Bee, and Opie are at the Hollywood studio watching a scene being filmed, when Andy mistakenly stands up and interrupts the filming we can see the wall and shelves behind the director, and it should look familiar because it's the wall and shelves from Floyd's shop in Mayberry.
Opie's Group - S8-E9
Andy: Clara, sometimes a parent can't see what he should do, and sometimes it takes a person from the outside to show him. And I'd like to thank you.
Clara: Groovy.
My Fair Ernest T. Bass - S4-E17
Trivia: At different points during this episode both Barney and Andy make the exact same comment, "If you wrote this into a play nobody'd believe it." This episode is based on My Fair Lady, which in turn is based on Pygmalion.
Question: Why is it when they were on the show the Darling sons never spoke? Would they be paid more if they did, or was this some sort of joke?
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.