Other mistake: After Barney gets annoyed over Andy's lack of confidence in his ability to be a sheriff, Barney gets on the phone with Sarah and asks to be connected to the mayor of Greendale, then it cuts to an exterior shot and the parked car has plate number "DC 269," the same as other vehicles in some earlier episodes.
The Andy Griffith Show (1960)
1 other mistake in Sheriff Barney - chronological order
Starring: Ron Howard, Don Knotts, Andy Griffith, Frances Bavier
Visible crew/equipment: When Otis tries to escape from Aunt Bee's clutches by hiding in the laundry service van, just as Aunt Bee has the driver open the van's back doors we can see the reflection of the moving boom mic in the left window.
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.
Trivia: In Walker's Drugstore, among all the magazines by the wall there's a TV Guide magazine (from Oct 9, 1954) on the shelf, and on its cover is Lucille Ball the co-owner of Desilu Productions - which produced TAGS, and also filmed at Desilu Studios.
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.