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.
Continuity mistake: After Andy and Floyd talk outside the grocery Floyd gets into his car with the convict, and when they drive away we see all the food ads taped to both of the store windows while Andy's on the sidewalk, but when it cuts to Andy's closeups the taped ads have changed.
Other mistake: Floyd's car has the license plate number "RD 757" which has been seen on other vehicles in previous episodes.
Character mistake: In the first scene of the show, Andy, Opie and the mayor are on a pier fishing a lake. They are casting with deep sea reels. If you've ever tried casting with a deep sea reel, it doesn't work out well. You can see there no equipment on the poles.
Revealing mistake: During the holdup at the bank, while the bank robber's holding Asa's broken gun, when Andy motions to Asa to duck out of the way in the closeup we can see the two thin wires to the left and right pulling the gun apart.
Visible crew/equipment: When Barney walks into the bank dressed as a woman, we can see the two curved chalk actor's marks on the floor behind the teller.
Barney and the Governor - S3-E15
Visible crew/equipment: After Barney has given the governor's chauffeur a parking ticket and the chauffeur drives off, just as Barney starts to say that he's not wearing the uniform to win friends, we can see the reflection of the boom mic at the top left corner of the screen.