Character mistake: In the beginning where Karen is introduced to Andy and Barney in the coffee shop, her name is Karen Worth, then at the last where she is called as winner of the Skeet Shoot her name changes to Karen Moore.
Suggested correction: She is introduced as "Karen Moore". Thelma Lou's pronunciation is a bit off (what she says sounds like 'moor', as in an English moor), but she says "Moore."
Aunt Bee's Brief Encounter - S2-E9
Other mistake: Mr. Wheeler's license plate number is 'DC 269' which has been used in earlier episodes. Then at the end, when the locks-keys man pulls his truck into the driveway, it has plate number 'VT 772' another prop plate seen in "Barney on the Rebound" when the pretty woman drives into town.
The Clubmen - S2-E10
Other mistake: After Andy turns down the offer to join the club the two men leave, and when it cuts to them driving away we see the license plate number is "DC 269," the same as some other vehicles in previous episodes.
Other mistake: Aunt Bee refers to losing the pickle contest 10 years in a row (which Clara corrects to 11, leading us to believe they have been in the same competition), but this is her 2nd year in Mayberry, having not seen Andy for years in her season 1 intro as the "new housekeeper", (or Opie - ever) in season 1.
Other mistake: When Andy, Barney, and Opie switch Aunt Bee's kerosene tasting pickles with the store bought pickles during 'operation pickle switch', they put the store pickles in Aunt Bee's mason jars with silver lids and Aunt Bee's pickles in the store's jars with labels and white lids. Their plan is to give away the store jars with Bee's pickles inside, and we see Barney placing the last of the store jars into his bag, but when Barney stops the driver to give him his safe driving award, we see Barney giving away the mason jars with silver lids even though it's the store jars he should be getting rid of.
Continuity mistake: When Andy locks himself in the jail cell, the key is lying flat on the short wall, but after Barney locks himself in the other cell, the key has turned itself upright on its side.
Other mistake: After Barney gets annoyed over Andy's lack of confidence in his ability to be a sheriff, Barney gets on the phone with Sarah and asks to be connected to the mayor of Greendale, then it cuts to an exterior shot and the parked car has plate number "DC 269," the same as other vehicles in some earlier episodes.
The Farmer Takes a Wife - S2-E13
Other mistake: At the end, when Joe Waters parks his car in the sheriff's parking spot his car's license plate number is "DC 269," which has been seen in earlier episodes on other vehicles.
The Keeper of the Flame - S2-E14
Continuity mistake: When Andy holds Barney by the shoulders while congratulating him for an outstanding job of detective work, Andy holds his notebook in his left hand, but when it cuts to a different angle the notebook's suddenly in Andy's right hand.
Continuity mistake: When Andy and Barney catch up with the man who ran Fletch's truck off the road, the rearview mirror suddenly vanishes in the closeups that face the windshield on Bailey's car.
Visible crew/equipment: When Barney's reading the Sunday comic strip Andy comes in to close the jail in the courthouse, and when Otis walks out of his cell we can see the actor's chalk mark on the floor where he stands.
Character mistake: When Barney walks by the barbershop window he glanced in and waves at Andy who is getting a manicure. But the man in the chair isn't Andy, it's a stand in. (00:17:00)
Visible crew/equipment: When the new manicurist tells Floyd that she works only on commission, she lifts the small table and moves it to the window, and we can see the actor's tape mark where she had just been standing.
Other mistake: When Barney and Andy find the trailer that Malloy's hiding in with his partner and Horton (who's tied up), the other trailer that Andy and Barney are standing behind has license plate "DC 269," the same as some other vehicles in previous episodes.
The Merchant of Mayberry - S2-E22
Plot hole: In the episode where Barney confronts the two farmers for selling produce on the side of the road, Barney mentions that they're not allowed to sell because of "section 17.4" of the ordinance code - that street vending is not allowed, and Andy confirms it. But in this episode Bert comes to town and is selling dry goods, etc. and he's allowed to sell. Even Ben states that there must be a structure if he's selling - wouldn't you think that Andy and Barney would have known that already before setting him up to sell?
Visible crew/equipment: When Otis tries to escape from Aunt Bee's clutches by hiding in the laundry service van, just as Aunt Bee has the driver open the van's back doors we can see the reflection of the moving boom mic in the left window.
Continuity mistake: When Otis begins his 24 hour sentence at Andy's house by staying in the guest room, Otis is wearing suspenders (braces) that are sewn together in the back in an X-shape, but when Otis leaves the guest room he's wearing entirely different style suspenders attached to his trousers.
Other mistake: The new game/hobby boxes that Barney hands out to the Gordon brothers have their brand names partially covered. Mr. Potato Head has 'Head' covered, the brand name of the leathercraft set is covered, and part of the name on the metalcraft tapping set is covered.
Andy and Barney in the Big City - S2-E25
Factual error: Though they are suppose to be in Raleigh, the skyline view is not Raleigh, NC.
Visible crew/equipment: When Barney and Thelma Lou leave Mary's house the curved chalk actor's mark is visible on the floor by the door. Then Barney shows up again with his drum, and we can see a chalk T-mark on the floor. That same T-mark is also there in a later scene, when Barney barges in with the letter he found behind the file cabinet.