Continuity mistake: At the "Hen Party", Jeff Pruitt says hello to Thelma Lou and she states she is going to get coffee, then goes to the kitchen. However, when Jeff walks across the room and looks back, Thelma Lou is back in the same area. She never walked back from the kitchen.
Continuity mistake: In the initial episode, and Runaway Kid in season 1, Barney is a cousin of Andy's. In subsequent episodes, they are unrelated.
Continuity mistake: Scenes shot at Andy's porch have significant differences depending on the filming location, as there are two sets of Andy's porch. One is just the facade of the house in the 'town of Mayberry' in the studio's 40 Acre backlot; and the second is located in the studio's soundstage. Note in some shots the door's sidelights have vertical muntin bars, the screen door has a white handle, whereas in other shots the sidelights' muntin bars are gone and the screen door handle is black (screen door's gone season 5). Also, note the significant difference in the width of the wall between the parlor windows and the door, the height of the parlor windows from the floor, etc.
Continuity mistake: The fuel pumps at Wally's gas station (regular and super) switch sides between numerous episodes.
Continuity mistake: As Barney is turning in his deputy equipment to resign his handcuffs are hanging out of his pocket. After Barney states he wishes someone would just commit a crime, Opie enters. As the camera pans out so Andy can ask Opie what happened, the handcuffs are no longer in Barney's pocket, and he didn't put them on the desk with the rest of the equipment. (03:03:00 - 03:11:00)
Continuity mistake: When Barney and Andy are looking at Barney's picture on the front page of the newspaper, first, the article has nothing to do with Barney or the arrest, and second, when Barney takes the paper from Andy he folds it with the front page on the outside, and the page we see is not the same front page from the closeup.
Continuity mistake: When Andy and Mrs. Silby are walking into the courthouse, in the exterior shot of Andy opening the door he's wearing the baseball mitt on his left hand, but when it cuts to the interior shot Andy's opening the door with his left hand and the mitt has vanished.
Continuity mistake: After Ellie tells the Taylors that she's withdrawing as candidate, when she and Andy head over to the rally at the hotel they pass the church, and in the long shot a large sign has suddenly appeared at the front of the church.
Continuity mistake: On one occasion when Mr. Weaver leaves the courthouse to walk around the building to look in through the cell window, he goes in a counterclockwise direction. However, when the scene switches he is approaching from a clockwise direction.
Mayberry Goes Hollywood - S1-E13
Continuity mistake: When Andy's done showing Hollywood producer Mr. Harmon around town, he says, "Here we are, right back where we started, old oak tree," then mentions climbing that tree as a boy, and later says, "You're gonna cut down the oldest oak tree in the entire town?" But viewers have seen the entire area in front of the church (season 1 "Ellie for Council") and there isn't a large old oak tree. The fake tree was placed in this episode as a plot point between the producer and the townspeople.
Mayberry Goes Hollywood - S1-E13
Continuity mistake: Barney's fancy new uniform has a badge on it when he first models it for Andy. During the ensuing festivities, it's missing.
Continuity mistake: While Andy and Barney are trying to sell the town cannon, when they're talking to the shop owner who's seated in the rocking chair we can see the area between the squad car and storefront, with various items for sale, but in the next shot the covered cannon has suddenly appeared - and it's tall enough to have been in view in the previous shot had it actually have been there.
Andy and the Gentleman Crook - S1-E21
Continuity mistake: After Gentleman Dan has taken Barney's gun, Aunt Bee, Opie, and Andy walk in on his attempted escape, and when Barney leaves the jail cell his badge inexplicably vanishes and reappears.
Andy and Opie, Housekeepers - S1-E23
Continuity mistake: When Aunt Bee leaves the house holding her suitcase, in the interior shot the suitcase lid faces out as Bee exits the front door, but in the next exterior shot the suitcase now faces the opposite way (note the rivets) as Bee continues to walk out the front door. (00:04:05)
Andy and Opie, Housekeepers - S1-E23
Continuity mistake: Andy is sitting on the couch, next to him on the end table is a glass and what appears to be a dark bottle like a beer bottle. They cut away, when they return to Andy on the couch the glass and the dark bottle have disappeared.
Continuity mistake: About 20 minutes in, Barney knocks the announcement bell off the door trying to sneak out of the pharmacy, Andy comes in one minute later and the bell rings when he opens the door. You can see the bell swinging above the door.
A Plaque for Mayberry - S1-E25
Continuity mistake: About 2/5 through the show, Barney comes into the office with a family tree chart. The edge of the paper is on the bottom of the roll sticking out to the left, there's a cut to a different angle and the edge of the paper is on top, not sticking out and still facing to the left. On top, it should be facing to the right.
Continuity mistake: After Frankie pays for the chewing tobacco in the drugstore, in the next closeup of Ellie the cigar box on the shelf behind her has black lines scribbled over all its identifying brand names (which is Van Dyck 43's), but when Frankie walks out the door, in Ellie's next semi-closeup that cigar box is unmarked again.
Continuity mistake: When Barney walks into the chicken coop there's a window on its door, but when Barney hides from Flint there's no such window on its door.
Continuity mistake: On Flint's farm there's a cow tied to the back fence, which can be seen in exterior shots throughout the episode - when Ellie, Andy, and Barney are there. After Flint tells Barney to get off his land, in the exterior shot when Barney walks into the barn we see that cow tied to the back fence, but next shot inside the barn we see that very same cow in the stall - note the black/white markings.
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.