Continuity mistake: When Andy and Barney catch up with the man who ran Fletch's truck off the road, the rearview mirror suddenly vanishes in the closeups that face the windshield on Bailey's car.
Continuity mistake: When Otis begins his 24 hour sentence at Andy's house by staying in the guest room, Otis is wearing suspenders (braces) that are sewn together in the back in an X-shape, but when Otis leaves the guest room he's wearing entirely different style suspenders attached to his trousers.
Andy and the Woman Speeder - S2-E3
Continuity mistake: At the end, when Andy and Barney are standing beside the woman's car her rear-view mirror has vanished in the closeups, but when she drives off in the long shot the mirror has reappeared.
Continuity mistake: When Andy locks himself in the jail cell, the key is lying flat on the short wall, but after Barney locks himself in the other cell, the key has turned itself upright on its side.
Continuity mistake: On the curb outside the courthouse there's a fire hydrant beside the pole, which not only changes its position on the sidewalk in different scenes, but it has also vanished at the end when Rogers drives away, as Barney crosses the street.
Continuity mistake: While the squad's siren switch is stuck in the on position, Barney and Rogers get out of the car to open the hood, and suddenly there's a pencil sticking out of Barney's shirt pocket for Rogers to use to tap the condenser box, to stop the blaring siren.
Mayberry Goes Bankrupt - S2-E4
Continuity mistake: In establishing scenes throughout the first part of the episode, Andy is seen driving up to Meyers' home which seems to be located far from neighbors and on a dirt road. In the "renovation" scene and those following, Frank's home is located on a paved road with other homes nearby in the shot. Clearly a different set entirely.
The Keeper of the Flame - S2-E14
Continuity mistake: When Andy holds Barney by the shoulders while congratulating him for an outstanding job of detective work, Andy holds his notebook in his left hand, but when it cuts to a different angle the notebook's suddenly in Andy's right hand.
Continuity mistake: When Barney disguises himself as an old woman, in the very first shot he's wearing a dress with lace and tiny flowers, but in all the following shots it's an entirely different dress with large groups of flowers. (00:17:40)
Andy and the Woman Speeder - S2-E3
Continuity mistake: When the woman speeder is seen, she is wearing sunglasses, which are gone in a later shot.
Continuity mistake: At the beginning of the show, Andy notices a wanted poster on the office bulletin board and tells Barney that he had learned from news accounts that the wanted person had been captured. Barney removes the poster and places it in a file cabinet. The next day when Roger reports for duty, he and Barney are looking at the bulletin board and the wanted poster is back up.
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.