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.
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.
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.