Visible crew/equipment: After Andy and Barney walk out of Floyd's shop, when Andy makes a crack about Barney's ears being uneven Andy walks offscreen, then Barney shouts at him as Andy's presumably already down the block, but in their reflection in the window behind them we can see that as soon as Andy walks offscreen in this closeup, he actually stops and leans over where we see the camera's located.
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)
Revealing mistake: When Barney pulls the jail cell window out of the exterior brick wall, as it's being yanked out we can see that the brick wall is only thin drywall during the stunt, as well as the fact that the wall around the breakage differs significantly between the closeup and wide shots.
Other mistake: Barney's cousin is coming to Mayberry but gets off the bus in a previous town and misses it. Barney and Andy go out to find him, leaving from Mayberry. They are driving down the road when they come upon his cousin. The cousin is walking in the same direction as Andy and Barney are going, which would have meant he was walking away from Mayberry when he should have been walking towards it.
Deputy Otis - S2-E31
Other mistake: Upon arriving at the courthouse, Andy and Barney discover they don't have their keys to get in so Andy decides to go knock on the window at Otis' cell, which he does to wake Otis. However, Otis' cell does not have a window, only the adjoining cell does. (00:20:00)
Suggested correction: Otis' cell does have a window. In the previous episode with Barney's cousin, Barney's pulls the window out of the wall to get Otis out. Also in another episode Barney gets an intercom and places one part by the window to demonstrate how it would work.
It has a window but no glass. It shows Andy knocking on the window to wake Otis up but then it shows him hanging on the bars.
Deputy Otis - S2-E31
Visible crew/equipment: After Otis admits to Andy the reason why his brother thinks that he works at the courthouse Otis walks back to the cell, but when Andy calls him back and gets up, just as Andy walks around the desk we can briefly see two actor's marks where they will stand momentarily.
Mr. McBeevee - S3-E1
Visible crew/equipment: When Barney, Andy and Opie go outside to see Opie's "horse" the microphone and boom shadow are visible on the back door.
Suggested correction: Those shadows are not from a microphone and boom pole. The shadows are from the overhang's open eave with its long rafter tail. Watch the opening scene (00:00:30) showing the back of the house, with its overhang above the back door and laundry line beside the house. Those shadows are also visible in this long shot.
Andy's Rich Girlfriend - S3-E2
Visible crew/equipment: After Andy explains to Barney why he's taking Peggy to a nice restaurant 55 miles away, when Barney walks away from the cell we can see the leg and shadow of the tall wood ladder (presumably the crew's) at the right side of the screen, but when Barney and Andy are by the front door there's no such ladder behind Barney in his closeups.
Andy's Rich Girlfriend - S3-E2
Continuity mistake: At the start, when both couples get in the squad car the rear-view mirror is gone in the closeup, but in other shots it's on properly.
Andy and the New Mayor - S3-E3
Visible crew/equipment: While Jess is up in the tree, the new mayor is attacked so he also starts climbing up the tree, then in the shot of the bear rushing toward the camera we can see the animal trainer who's behind the tree, as he releases the bear. (00:23:00)
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.
Deliberate mistake: Luke's dog in the episode is the same dog used in other episodes involving a dog in the plot.
Other mistake: When Barney is ready to pour the plaster cast into the shoe prints, there are only a few prints on the ground. There should be a continuous set of prints from the barn door to wherever.
Barney Mends a Broken Heart - S3-E6
Visible crew/equipment: While Andy and Barney are with Daphne and Skippy at the Tip-Top Cafe in Mount Pilot, when Daphne's boyfriend walks in we can see the actor's chalk T-mark on the floor.
Visible crew/equipment: While the fake band members begin to practice before the mayor shows up, in Andy's closeup right before he tries to stop Phil's flamboyant playing, the reflection of filming equipment is visible on the surface of Andy's tuba.
Visible crew/equipment: At the start, when Andy and the rest of the band are at Floyd's, we can see the black tape mark on the floor behind the barber's chair where Floyd's standing. Watch Floyd walk away from the chair for a moment, and when he goes back he looks down twice to make sure he's standing at his mark.
Continuity mistake: When the mayor finally arrives for the band's marching performance he parks his white car in front of the wood bench where he'll be sitting in a moment. After the fake band's performance, when the mayor tells Andy that the band can go to the band festival, in the shot of the real band members cheering while Andy pats the mayor on the back and also when the Fleet Band drives by, we can see the entire street in front of the mayor and his car has vanished.
Floyd, the Gay Deceiver - S3-E9
Continuity mistake: At the start, when Floyd and Andy walk into the barbershop, in the exterior shot Floyd's white barber jacket is on a hanger hanging from the coat tree that has a finial at the top of its pole, but in the next interior shot that jacket is hanging directly on the coat tree's hook, the hanger has vanished, and that finial has disappeared as well.
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.
Continuity mistake: While Peggy's waiting in front of the drugstore she's splashed by a car driving through a puddle, and when she shows up at Andy's house the stains on her dress are different.
