Continuity mistake: When Aunt Bee, Andy, Ollie, and Nora are in the kitchen for breakfast, the bag of flour vanishes from the counter depending on the angle of the shot.
The Education of Ernest T. Bass - S5-E4
Continuity mistake: In Season 3, Mountain Wedding, Earnest T knows how to read and write. He writes a letter to Andy and uses a rock to throw it in. In The Education of Ernest T Bass, we are told that Ernest T cannot read nor write.
Continuity mistake: Barney tries showing Andy what the "part bloodhound" dog can do for The Manhunt so Barney blows a dog whistle, and in the closeups of the growling dog the rope that was tied to his collar is suddenly lying on the floor, but it's back on his collar in the following shot.
Continuity mistake: When Barney, Thelma Lou, and Andy are driving to Andy's blind date they're all in the squad car. When they're parked in front of Helen's house in the closeup shots the light mounted on the roof has vanished, the glass windshield's gone, the car's interior differs, etc., and then it changes back. The roof is black, then white, as well.
Continuity mistake: After Andy convinces Barney to take off the uniform and wear his suit, when they pull up to the courthouse in the squad car the rear-view mirror is on properly, but in the shot facing the windshield the mirror has vanished, and then it reappears.
Goodbye Sheriff Taylor - S5-E10
Continuity mistake: While Barney's trying to instruct the new deputy candidates, when he throws a tomato to Otis it splatters on his shirt, and a few things keep changing depending on the angle of the shot - the amount of tomato goo increases/changes position; the suspender's sliding adjuster changes height; the deputy badge changes position.
The Pageant - S5-E11
Continuity mistake: While Andy and Opie are sitting on the couch, Andy's on the phone talking about having to tell Aunt Bee to drop out of the play, and there are two candlesticks with candles on the server behind Andy, but in Andy's closeups they're gone.
Continuity mistake: While the Darlings are at Andy's house the first time, on the hutch that's against the wall behind the sofa, there's a vase on the left side of the bottom shelf which vanishes and reappears.
If I Had a Quarter Million Dollars - S5-E22
Continuity mistake: After Barney makes his way around town spreading The Rumor that he has loads of money, when Barney walks into the courthouse he removes his jacket and hat then hangs them on the coat tree, and the hat keeps moving under and over the jacket between shots.
Continuity mistake: In the exterior shots of the bank's doors there are rectangular door knob backplates on the outside of the door, but in the interior shots when the door's open we can see the door knob's backplate is narrower and has a decorative top.
Continuity mistake: When Barney walks into the bank and turns on the light, we can see there's no damage to the side of the door, but when Andy walks in he points out the area where the door was jimmied.
Continuity mistake: When Barney's outside the bank loading his gun with the bullet, there are window blinds on the inside of the doors' windows - nothing else, but when Barney's inside the bank there are white shades between the glass panes and the blinds. As for the bank's large side window the opposite happens - there's a white shade between the pane of glass and blinds in the exterior shot, but in the interior shots we can see through the blinds' slats and there's no shade.
The Arrest of the Fun Girls - S5-E28
Continuity mistake: When Helen and Thelma Lou walk into the courthouse and find Andy and Barney dancing with Daphne and Skippy, there are lipstick marks on Barney's cheek, but when Andy gives Skippy her sweater and radio then tells them both to go, in the closeups the lipstick marks are gone, though they reappear momentarily.
The Arrest of the Fun Girls - S5-E28
Continuity mistake: When Daphne and Skippy drop in on Andy and Barney at the courthouse and want to "play jail," Skippy carries the radio and her sweater into the jail cell with her, but when Skippy asks for her ukulele we see the radio and sweater are now on the side desk, under the gun case.
Opie Flunks Arithmetic - S5-E30
Continuity mistake: At the end, when Helen shows up at the courthouse and tells Andy that Opie got a B+ on the test, her purse vanishes and then reappears while she's sitting on the banister beside the desk.
Opie Flunks Arithmetic - S5-E30
Continuity mistake: When Barney, Andy, and Aunt Bee are at the table after Opie goes upstairs to study, in shots that face all three of them there are things on the middle shelf to the left and right of the center plate, but then in other shots either the left item is gone, or the right item is gone.
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.