Aunt Bee's Invisible Beau - S5-E27
Revealing mistake: When Clara and Aunt Bee are talking in the kitchen, in the closeups facing Aunt Bee we see the counter, the cabinet, and the wall, but what we don't see are the curtains, the window, or the windowsill, which all should be on that wall. The fake window wasn't placed on the set wall for Bee's closeup.
Visible crew/equipment: While Ollie's making up excuses to rush home, he and Nora are saying goodbye to Aunt Bee, and the reflection of the moving boom pole and mic are visible on the car's windshield.
Goodbye Sheriff Taylor - S5-E10
Continuity mistake: While Barney's trying to instruct the new deputy candidates, when he throws a tomato to Otis it splatters on his shirt, and a few things keep changing depending on the angle of the shot - the amount of tomato goo increases/changes position; the suspender's sliding adjuster changes height; the deputy badge changes position.
Revealing mistake: At the end, in the shots of the kids dancing in class, the width of the wall between the shelf/coat hooks and the perpendicular wall with the door has bizarrely increased by 1-2 feet, but that extra width is gone in previous and following shots. Presumably they needed extra space for all the kids to dance so they moved that left wall.
The Pageant - S5-E11
Continuity mistake: While Andy and Opie are sitting on the couch, Andy's on the phone talking about having to tell Aunt Bee to drop out of the play, and there are two candlesticks with candles on the server behind Andy, but in Andy's closeups they're gone.
Three Wishes for Opie - S5-E14
Other mistake: When Andy asks Floyd and Judd about who he's supposedly marrying it cuts to Helen walking down the street, and the grocery store has only one display window, when it should have two windows, and there's a brick wall adjacent to the window which shouldn't be there. (Shot at the soundstage not backlot).
Revealing mistake: While Barney's explaining to Andy his new interest in realty they both walk to the back room, and just as they pass through the doorway the camera tracks too far to the left, so we can see the edge of the set wall and the rest of the back wall is missing. (The following shot is from the direction of that missing wall).
Barney Runs for Sheriff - S5-E21
Other mistake: When Floyd tells Barney that he doesn't want to put Barney's campaign poster in the barbershop window because it spoils the decor, the reflection we see in the mirror behind Floyd is the church's front door and steps. This makes no sense at all because the reflection should be whatever is to the right of Floyd's, but the church is the opposite way - to the left, past the courthouse. The view in the mirror is a painted backdrop, but it's still quite wrong.
The Arrest of the Fun Girls - S5-E28
Continuity mistake: When Helen and Thelma Lou walk into the courthouse and find Andy and Barney dancing with Daphne and Skippy, there are lipstick marks on Barney's cheek, but when Andy gives Skippy her sweater and radio then tells them both to go, in the closeups the lipstick marks are gone, though they reappear momentarily.
Opie Flunks Arithmetic - S5-E30
Continuity mistake: At the end, when Helen shows up at the courthouse and tells Andy that Opie got a B+ on the test, her purse vanishes and then reappears while she's sitting on the banister beside the desk.
Opie Flunks Arithmetic - S5-E30
Continuity mistake: When Barney, Andy, and Aunt Bee are at the table after Opie goes upstairs to study, in shots that face all three of them there are things on the middle shelf to the left and right of the center plate, but then in other shots either the left item is gone, or the right item is gone.
Continuity mistake: Barney tries showing Andy what the "part bloodhound" dog can do for The Manhunt so Barney blows a dog whistle, and in the closeups of the growling dog the rope that was tied to his collar is suddenly lying on the floor, but it's back on his collar in the following shot.
Continuity mistake: When Barney, Thelma Lou, and Andy are driving to Andy's blind date they're all in the squad car. When they're parked in front of Helen's house in the closeup shots the light mounted on the roof has vanished, the glass windshield's gone, the car's interior differs, etc., and then it changes back. The roof is black, then white, as well.
The Arrest of the Fun Girls - S5-E28
Continuity mistake: When Daphne and Skippy drop in on Andy and Barney at the courthouse and want to "play jail," Skippy carries the radio and her sweater into the jail cell with her, but when Skippy asks for her ukulele we see the radio and sweater are now on the side desk, under the gun case.
Goober Takes a Car Apart - S5-E17
Factual error: Halfway through the show, Goober takes the motor out of the car and they start it up in the Sheriff's office. If you look at the direction of the fan, it would be blowing the air forward instead of towards the rear of the engine. It would be fighting the air coming through the radiator instead of pulling it.
Continuity mistake: In the exterior shots of the bank's doors there are rectangular door knob backplates on the outside of the door, but in the interior shots when the door's open we can see the door knob's backplate is narrower and has a decorative top.
Other mistake: In this episode (aired Sep. '64) Barney tells Andy that 5 years ago on May 16 (1959) he joined the sheriff's office, and later they all have a surprise party for Barney. However, in season 4 "Citizen's Arrest" (aired Dec. '63) Andy tells Barney that he found, "The custody receipt for the first revolver I issued you... August, 1953... 10 years ago last month since I swore you in." Andy even mentions having a party with a cake that has 10 candles on it.
Three Wishes for Opie - S5-E14
Revealing mistake: Barney, convinced he can foretell the future, is in the darkened jailhouse, seated between Goober and Floyd at a table. Goober strikes a match and lights a lamp which is directly in front of Barney. The immediate illumination obviously comes from a studio light because the men's shadows on the wall are to the far left of the men, instead of directly behind them.
Continuity mistake: While the Darlings are at Andy's house the first time, on the hutch that's against the wall behind the sofa, there's a vase on the left side of the bottom shelf which vanishes and reappears.
Three Wishes for Opie - S5-E14
Other mistake: When Barney uses the gypsy lamp and cards in the back room, in the shots with Goober and then with Opie while they're standing in the doorway, the wall opposite them has a barred window, but in earlier episodes that wall has the door that leads outside to the side of the building.
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.