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.
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 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.
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.
Other mistake: Notice the license plate of Rogers' car is "DC 269," which is the same plate number as Andy's squad in a few season 1 episodes such as "Ellie Comes to Town" and "A Feud is a Feud."
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.
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.
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 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.
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.