Opie's Job - S6-E1
Visible crew/equipment: When Goober walks up to Andy outside the grocery/meat store, before Goober picks up the apples we can see a chalk mark on the ground between his feet.
Opie's Job - S6-E1
Other mistake: In the scenes outside the grocery store with Mr. Doakes, there are a couple dozen cereal boxes in the display windows - Post Grape Nuts, Post Grape Nuts Flakes, Post Alpha Bits, etc., and all the boxes have part of their names covered, such as "Rap Ut." It's pretty funny considering that TAGS cast did commercials for Post Grape Nuts, and other Post foods.
Opie's Job - S6-E1
Continuity mistake: When Aunt Bee walks by Floyd's shop the barber's pole is missing, but when Opie and Billy run across the street there's a red/white striped barber's pole, then when Andy walks by Floyd's shop the barber's pole has red/white/blue stripes.
Opie's Job - S6-E1
Continuity mistake: We see the exterior of the grocery/meat store a few times during this episode, and there are differences in things such as the actual facade of the building, the view through the doorway, etc.
Opie's Job - S6-E1
Continuity mistake: When Opie and Billy are both heading to the grocery store to apply for the job, the church is behind the boys and they're standing in front of the 'new and used furniture' store - both of which are to the right of the courthouse (when facing the courthouse), and to the left of the courthouse are the barbershop and the grocery/meat store.When the boys run across the street, they're coming from the opposite direction.
Andy's Rival - S6-E2
Other mistake: After Helen calls Andy to cancel their date, it cuts to Goober and Andy walking down the street and there's a brick wall adjacent to the grocery/meat store which should not exist.
Malcolm at the Crossroads - S6-E3
Continuity mistake: When Andy rushes up to Ernest T. and tells him to quit throwing rocks at the car, Ernest T. holds the crossing guard sign with his left hand and points at it with his right hand, but in the closeup it's vice versa. (00:01:00)
Malcolm at the Crossroads - S6-E3
Continuity mistake: At the start, Andy walks down the street and stops at the church steps to watch Ernest T. being a crossing guard, but when it cuts to the shot of Ernest T. we see the church steps yet Andy's gone, then when it cuts back to Andy he's still standing by the church steps.
Visible crew/equipment: When Floyd and the other men are with John Canfield joking about Floyd's barber skills, a chalk T-mark is visible on the ground by the man with his foot on the bench. Then when Canfield walks away we can see more chalk marks on the ground.
Other mistake: When John Canfield's talking to Floyd, Andy, and the other men they're in front of the display window, which doesn't have any panes of glass.
The Bazaar - S6-E5
Continuity mistake: After Goober complains to Andy about Warren it cuts to Warren walking down the street, and when he moves the bucket of corn in front of the grocery store, the window display and the taped signs change/vanish between shots. (00:02:05)
The Bazaar - S6-E5
Visible crew/equipment: After Andy shouts at Goober to get his pickup truck away from the courthouse, it cuts to Andy, Warren, and all the women in the courthouse, and we can see the chalk T-mark on the floor at Warren's feet.
The Bazaar - S6-E5
Continuity mistake: When Andy looks out the courthouse window and sees Goober's pickup truck filled with the ladies auxiliary group, Andy rushes out the front door and there's a wall right behind him where there shouldn't be, and although there's a bulletin board on the wall it still differs from the real one, plus the wall's air vent and wall trim are missing.
Continuity mistake: When Goober and Warren are at the diner, things on the counter keep switching places while Goober eats his peanut butter, tuna, and ketchup sandwich. (00:09:00)
Other mistake: While Andy and Helen are rearranging everything in the squad car's trunk to make it all fit, Helen picks up the large thermos and written on its bottom we see "Reggie personal." Reggie Smith was property master on set. (00:12:45)
Visible crew/equipment: After Goober has deliberately removed the distributor cap from Andy's squad car, when Andy slams the hood shut we can see the reflection of the filming crew on Floyd's window. Then when Andy and Helen drive away in Goober's truck, the microphone pops up into view at the bottom of the screen. (00:17:20)
Continuity mistake: When Warren parks the squad car at the bus stop, as he gets out of the car note the long whip antenna is attached to the bracket over the rear passenger door, but when it cuts to the closeup the whip antenna has vanished. (00:21:25)
Revealing mistake: When the bus pulls up for the Taylor family to leave for Hollywood you can see behind the bus a California freeway with cars moving in both directions. I don't think that Mayberry had a freeway right outside town. The scene is fixed when they return in "Aunt Bee on TV." There has been a tree put there so the road wouldn't show.
The Taylors in Hollywood - S6-E8
Visible crew/equipment: After the studio's security guard tells Andy they're filming on stage 40, when it cuts to the Taylors walking onto the set we can see two chalk T-marks on the floor (one in front of Andy's feet). (00:13:00)
The Taylors in Hollywood - S6-E8
Revealing mistake: While the Taylors are watching the scene being filmed of the attempted jailbreak Gavin MacLeod plays the sheriff, but while he's fighting the Calhoun brothers it's the actor's stunt double who's actually doing the fighting. (00:17:45)
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.