Continuity mistake: When Opie surprises Andy by telling him that he wants to take piano lessons with Clara, he heads to the piano to play what he already knows, and when Opie plays Chopsticks on the piano he's wearing a different shirt.
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.
Visible crew/equipment: While Andy and Otis are talking about women Barney opens the door and rushes into the courthouse, and behind him we can see a crew member's hand (looks like a woman wearing bracelets) catching the door as Barney swings it shut.
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 Ill-Gotten Gain - S4-E8
Continuity mistake: Andy reads the inside cover of Barney's old schoolbook which has Barney's name "Bernard P. Fife" written out many times in it, but in two previous episodes Barney's middle name is either Oliver or Milton.
Continuity mistake: After Frankie pays for the chewing tobacco in the drugstore, in the next closeup of Ellie the cigar box on the shelf behind her has black lines scribbled over all its identifying brand names (which is Van Dyck 43's), but when Frankie walks out the door, in Ellie's next semi-closeup that cigar box is unmarked again.
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.
Visible crew/equipment: When the squad's siren gets stuck blaring, a crowd gathers around the squad with Andy, Barney and Rogers, and when the crowd disperses we can see at least three chalk T-marks on the ground.
Andy and Opie - Bachelors - S3-E4
Revealing mistake: After Andy and Opie choose between chicken and pot roast using a nickle, when Opie gives the nickle back to Andy the window over the sink is missing - the fake window wasn't put up on the set wall for this shot, but when the food burns the window and curtains are up there as usual.
Visible crew/equipment: At the Scobey house, after Ben sits in the unstable chair and it breaks, when Andy and the Scobeys rush over to him we can see the two curved chalk actor's marks on the floor, where Ben had been standing moments before.
Continuity mistake: In this episode, during the scenes at Thelma Lou's house the front door is right beside a wall perpendicular to it, but in earlier and later episodes the front door is beside the dining room at the opposite side of the parlor.
Continuity mistake: While Andy and Barney are trying to sell the town cannon, when they're talking to the shop owner who's seated in the rocking chair we can see the area between the squad car and storefront, with various items for sale, but in the next shot the covered cannon has suddenly appeared - and it's tall enough to have been in view in the previous shot had it actually have been there.
Visible crew/equipment: When the new manicurist tells Floyd that she works only on commission, she lifts the small table and moves it to the window, and we can see the actor's tape mark where she had just been standing.
Aunt Bee's Big Moment - S8-E23
Visible crew/equipment: After Aunt Bee's solo flight, just as the flight instructor walks over and gives Bee the papers as proof that she soloed, the large T-mark (rubber/plastic) is visible on the ground between Bee and the instructor.
A Plaque for Mayberry - S1-E25
Visible crew/equipment: While everyone's waiting for Otis to arrive at the plaque presentation in Mayor Pike's office, after Andy admits to the mayor that he asked the real Otis to show up, it cuts to the mayor walking behind his desk, and we can see the chalk T-mark on the floor where Mrs. Bixby stands.
Runaway Kid - S1-E6
Visible crew/equipment: After Andy talks to George's father on the phone, he gets up and stands near the fireplace while explaining to Opie why he broke his promise and called George's father, and when Opie's on the couch asking if he can run off sometime, we can see the white tape mark on the rug where Andy was standing moments ago.
My Fair Ernest T. Bass - S4-E17
Revealing mistake: At the start, when Ernest T. throws the rock at Mrs. Wiley's window and it breaks, the area around the hole flutters in the breeze - it's obviously not a glass window used for the stunt.
Aunt Bee's Invisible Beau - S5-E27
Revealing mistake: When Clara and Aunt Bee are talking in the kitchen, in the closeups facing Aunt Bee we see the counter, the cabinet, and the wall, but what we don't see are the curtains, the window, or the windowsill, which all should be on that wall. The fake window wasn't placed on the set wall for Bee's closeup.
Continuity mistake: While Aunt Bee and the party guests are gathered in the parlor, when Gomer hoots like an owl in the shot facing him note Floyd's eyeglasses - black with thick straight temples, but in the shot from behind Gomer and all following shots Floyd's wearing different eyeglasses - lighter color with curved tips.
Visible crew/equipment: While Ollie's making up excuses to rush home, he and Nora are saying goodbye to Aunt Bee, and the reflection of the moving boom pole and mic are visible on the car's windshield.
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.