Aunt Bee and the Lecturer - S8-E10
Visible crew/equipment: When Andy parks the squad car in front of the house he asks Hubert about the picnic, and the reflection of the moving boom mic is visible on the windshield. (00:12:35)
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)
Visible crew/equipment: At the end, while the foursome sit around drinking pop, in the very last shot of Howard we can see the reflection of filming equipment in the window, before the shot fades. (00:24:30)
The Education of Ernest T. Bass - S5-E4
Continuity mistake: In Season 3, Mountain Wedding, Earnest T knows how to read and write. He writes a letter to Andy and uses a rock to throw it in. In The Education of Ernest T Bass, we are told that Ernest T cannot read nor write.
Character mistake: When Barney walks by the barbershop window he glanced in and waves at Andy who is getting a manicure. But the man in the chair isn't Andy, it's a stand in. (00:17:00)
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.
Deliberate mistake: Gomer leaves the woods after they were lost and doesn't have anything with them then when they get to the campsite he has the snare that they made.
Continuity mistake: In this episode, Ernest T writes Charlene a love letter. In a later episode when Ernest T goes back to school, it is revealed that he can neither read nor write.
Visible crew/equipment: At the end when Aunt Bea enters the courthouse, she doesn't close the door completely. You can see a hand from outside grab the door, and close it very slowly. (00:23:20)
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.
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)
Factual error: December 25, 1960 was on Sunday. The calendar in the jail house shows a calendar (which has been used in other episodes) with Christmas Day on a Friday. (01:30:00)
Opie's Group - S8-E9
Audio problem: The band Opie is in has two guitar players but no bass player, even though you can hear a bass guitar being played.
Other mistake: When Barney is ready to pour the plaster cast into the shoe prints, there are only a few prints on the ground. There should be a continuous set of prints from the barn door to wherever.
The Gypsies - S6-E23
Factual error: The Gypsies manage to operate a shortwave radio without an antenna or AC power.
Continuity mistake: When Otis makes up a poem about jumping rope, Barney lets go of the rope and Andy is left holding the other end while the rope is left stretched across the floor. One second later when Opie and his friend come running in, Andy is now holding the rope in his other hand all rolled up.
Revealing mistake: The woman in the foreground, as the siren is stuck, is carrying a paper grocery sack from "Hollywood Ranch Market" which was located on Vine St and Fountain Ave in Hollywood, Los Angeles. (00:09:35)
Factual error: We know from 2 episodes prior (Man in a Hurry) and generally mentioned throughout the show, the only filling station in Mayberry is Wally's Filling Station. In this episode Mayor Stoner is accused of only putting the new underpass in Mayberry because it will be next to Mayor Stoner's brother's filling station.
Continuity mistake: The fuel pumps at Wally's gas station (regular and super) switch sides between numerous episodes.
Plot hole: When Barney and Andy are on the street watching the window painter, Andy looks over and says "I believe that's Briscoe Darlin's truck!" - but when they were driving up to his place the next morning, they both got out of the car and were wondering where their house was they heard music playing. The next scene shows them pulling in - seems that if he was able to recognize the truck in town, he would have been able to recognize the truck and they could have drove around looking until they found it?
Answer: As noted in the previous answers, in real life, things like this provided wind and/or rain deflection, and also maintained a bit of privacy when blinds were raised somewhat. The interior courthouse set was located in the studio, so the "outside" Main Street didn't exist. I believe these things were added to the courthouse windows for practicality, to avoid some crew movement being visible on the opposite side of those windows. These are not "window boxes" to hold anything, as they're actually bottomless; we can see the Venetian blind's long pull cords under them. They're made of plywood and simple to build, so the "material and labor" was inexpensive. Similar variations made of different materials are in other movies/shows. In 1957's "12 Angry Men," textured chicken wire glass panels are in the jury room windows, and in "Jesse Stone: Night Passage" another type is in Jesse's office windows.
Super Grover ★