Continuity mistake: While Barney's on the farm trying to get Frankie, twice he heads into the barn through the right-side entrance door within the tall sliding double barn doors (about 12 ft high), but when it cuts to the interior shots he's entering through the barn's left-side entrance door, plus the fact that it's not within huge double sliding doors. (This interior set is seen again in "Barney Gets His Man.").
Continuity mistake: After Eddie Brooke offers Barney five dollars and asks to be let go, it cuts to the State Police car passing the "drugs prescriptions" storefront, then Barney and Eddie trip and scuffle for two consecutive shots, and when it cuts back to the State Police car they haven't even passed that storefront yet. Additionally, that storefront is only two stores down from the coffee shop where Barney and Eddie are.
Continuity mistake: On the curb outside the courthouse there's a fire hydrant beside the pole, which not only changes its position on the sidewalk in different scenes, but it has also vanished at the end when Rogers drives away, as Barney crosses the street.
Continuity mistake: While the squad's siren switch is stuck in the on position, Barney and Rogers get out of the car to open the hood, and suddenly there's a pencil sticking out of Barney's shirt pocket for Rogers to use to tap the condenser box, to stop the blaring siren.
Continuity mistake: At the beginning of the show, Andy notices a wanted poster on the office bulletin board and tells Barney that he had learned from news accounts that the wanted person had been captured. Barney removes the poster and places it in a file cabinet. The next day when Roger reports for duty, he and Barney are looking at the bulletin board and the wanted poster is back up.
Andy and the Woman Speeder - S2-E3
Continuity mistake: At the end, when Andy and Barney are standing beside the woman's car her rear-view mirror has vanished in the closeups, but when she drives off in the long shot the mirror has reappeared.
Andy and the Woman Speeder - S2-E3
Continuity mistake: When the woman speeder is seen, she is wearing sunglasses, which are gone in a later shot.
Mayberry Goes Bankrupt - S2-E4
Continuity mistake: In establishing scenes throughout the first part of the episode, Andy is seen driving up to Meyers' home which seems to be located far from neighbors and on a dirt road. In the "renovation" scene and those following, Frank's home is located on a paved road with other homes nearby in the shot. Clearly a different set entirely.
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.
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.
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.
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)
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.
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.
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.
Continuity mistake: In the closeup of Barney's yearbook picture his name is listed as "Bernard Milton Fife," and Andy even reads it aloud, but in the previous episode from season 1, "A Plaque for Mayberry" Andy says that Barney's middle name is Oliver.
Aunt Bee's Medicine Man - S3-E24
Continuity mistake: The pillow on the right side of the couch is there while Opie is talking to the Colonel. When Andy walks around after Opie leaves, it has suddenly disappeared. (00:16:00 - 00:18:00)
Answer: Those "boxes" are valences that used to be very common, before air conditioning. They allow for windows to be open during rain storms. They permit air circulation, without letting the rain in.