Mayberry Goes Hollywood - S1-E13
Revealing mistake: When Andy is listening to the Hollywood producer talking about how he wants the town back the way it was before, over Andy's shoulder the "window" in one of the stores is blowing in the wind.
A Plaque for Mayberry - S1-E25
Continuity mistake: About 2/5 through the show, Barney comes into the office with a family tree chart. The edge of the paper is on the bottom of the roll sticking out to the left, there's a cut to a different angle and the edge of the paper is on top, not sticking out and still facing to the left. On top, it should be facing to the right.
Floyd, the Gay Deceiver - S3-E9
Other mistake: In the final scene near the end of the episode Floyd calls Andy "Andy Griffith". It's muffled, but if you listen closely it's audible.
Revealing mistake: On most of the corners of the buildings, you can see seam lines running down between the different sides of the buildings. The bricks on the opposite sides usually don't line up with each other either even though they are supposed to be the same brick.
Revealing mistake: At about 1:15 into the show, as they walk past the train station ticket window, you can see daylight between the wall of the ticket window and the rest of the building, showing it's just a prop building. It's fixed the next time they walk past it.
A Black Day for Mayberry - S4-E7
Character mistake: When Opie comes in at the beginning of the episode and asks where Andy is, the exchange ends with Barney asking "Something you want to see him about?" and Opie replying "No, I'll wait," which makes no sense in context. It would have made more sense if Barney had asked "Do you want to leave him a message?"
Visible crew/equipment: At the end, when Dr. Breen tells the very tired group, "You all look as serene and relaxed as if you'd just finished listening to a pleasant band concert," in the next shot facing the porch, the shadow of the boom mic is moving around between the two windows above Clara and Andy, at the top of the screen.
Continuity mistake: In earlier episodes, we are told that Gomer can't do mechanic work. He just pumps gas and air: "There's no charge for air; air is free; we don't make no charge for air." But in this episode, Gomer has become an ace master mechanic.
The Darlings Are Coming - S3-E25
Continuity mistake: When Briscoe gets into his truck, his hat is wet from dipping it (5x) in a horse trough. The camera cuts away to Andy and immediately back to Briscoe, whose hat is now dry. Also, "she's always hood for 11 hat fulls," yet Briscoe only puts 5 hats of water in his engine.
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)
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)
Visible crew/equipment: When Barney and Andy are waiting for Virgil to arrive, just as the bus pulls up and stops, the reflection of the boom pole/mic is visible on the windshield. (00:03:50)
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.
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)
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).
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)
Andy and Opie, Housekeepers - S1-E23
Continuity mistake: When Aunt Bee leaves the house holding her suitcase, in the interior shot the suitcase lid faces out as Bee exits the front door, but in the next exterior shot the suitcase now faces the opposite way (note the rivets) as Bee continues to walk out the front door. (00:04:05)
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)
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.
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.