Visible crew/equipment: At the start, while Aunt Bee is ironing the bowling shirt, a chalk T-mark is visible on the floor under Opie's chair.
Visible crew/equipment: When everyone is at the airport before the flight some chalk T-marks are visible on the floor, such as the one between Andy and Helen when Andy takes the picture of Aunt Bee and her friends. (00:08:45)
Visible crew/equipment: After Andy hatches the plan to have Aunt Bee and her friends pick up their photos at the same time, in the following shot just as Andy walks into the shop, the shadow of the boom mic is moving beside the doorway, at the top left side of the screen.
Visible crew/equipment: After Aunt Bee's flight lands, when it cuts to the hotel lobby there's rug on the floor extending from the front desk to the stairs, but in the next shot as Aunt Bee and her friends walk into the lobby that rug is gone (this doesn't refer to the small rug behind them). Also note the tape mark on the floor where the bellhop stops the luggage trolley.
Andy's Trip to Raleigh - S8-E4
Visible crew/equipment: When Andy gets back from Raleigh and shuts the car door, just as the camera moves in closer we can see the reflections of two crew members (the one wearing a yellowish shirt looks as if he's pushing the camera dolly), on the window behind Andy.
Opie Steps Up in Class - S8-E5
Visible crew/equipment: When Andy walks into the living room at the Hollander's house, the white tape mark is visible on the floor between Andy's and George's feet.
Opie Steps Up in Class - S8-E5
Visible crew/equipment: When Aunt Bee picks Opie up at Billy's house, while Opie tells her all about lunch we can see the reflection of the camera and crew member, on the car's vent window.
Opie Steps Up in Class - S8-E5
Visible crew/equipment: When Aunt Bee drops Opie off at Billy Hollander's house, just as Opie opens the car door the reflections of a crew member and filming equipment are visible on the door's surface.
Visible crew/equipment: After the shot of Milly holding hands with Howard (holding a picnic basket), when it cuts to Goober sitting in front of the courthouse the camera angle is low, so the wood framework and lighting equipment at the top of the courthouse set is visible, just as Andy walks over to Goober. (00:05:30)
Opie's Group - S8-E9
Visible crew/equipment: After Opie leaves Emmett's shop it cuts to the Taylor dining room as Opie is walking away from the server with salt/pepper shakers, and when he sits down we can see the actor's tape mark on the floor by the server. (00:06:25)
Opie's Group - S8-E9
Visible crew/equipment: While Opie and his band are playing at the party there are shots of the kids dancing, and in the shot of a girl with blonde hair wearing a blue dress, the camera angle is low and we can see the top of the set. (00:10:25)
Opie's Group - S8-E9
Visible crew/equipment: After Aunt Bee asks Clara to speak to Opie, in the interior shot just as Clara walks into the house we can see the two tape marks on the floor, where Clara and Opie will stand.
Aunt Bee and the Lecturer - S8-E10
Visible crew/equipment: When Andy parks the squad car in front of the house he asks Hubert about the picnic, and the reflection of the moving boom mic is visible on the windshield. (00:12:35)
Visible crew/equipment: At the end, while the foursome sit around drinking pop, in the very last shot of Howard we can see the reflection of filming equipment in the window, before the shot fades. (00:24:30)
Visible crew/equipment: When Aunt Bee heads out for her first cooking show at the studio, Andy and Opie help load Bee's car, then just as Bee walks around the front of her car, we can see the reflection of various production equipment on the surface of the car. (00:08:00)
Visible crew/equipment: When Aunt Bee comes home enraged at the butcher, a white tape mark is visible on the floor near the kitchen door (it wasn't there in a previous shot).
Emmett's Brother-in-Law - S8-E18
Visible crew/equipment: When Ben accompanies Emmett on his first call to Andy, just as they both enter the courthouse, we can see a crew member's hand outside reach out to catch the door as it closes. (00:12:40)
The Church Benefactors - S8-E20
Visible crew/equipment: At the start, Andy's trying to get Opie's hair to stay down, and when Aunt Bee appears on the stairs, the moving boom mic casts a shadow at the top left corner of the screen. (00:00:30)
The Church Benefactors - S8-E20
Visible crew/equipment: At the start of the finance committee meeting, when Clara walks into the office modelling the choir robe, the shadow of the boom mic is visible on the door, in the top right corner of the screen. White tape marks are also visible on the floor, as Clara twirls in the choir robe. (00:08:15)
The Church Benefactors - S8-E20
Visible crew/equipment: During the meeting with the finance committee, a chalk T-mark is visible near Howard's feet when he and Emmett demonstrate their building and safety committee proposal.
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.