Factual error: When you walk into the courthouse the first jailhouse to the left has a window. But the courthouse is connected to another establishment on that side. A window would be impossible.
Factual error: The badges they wear don't match the badges on their patches. If there's a badge on the patch, it's supposed to match their actual badge.
Factual error: A town like Mayberry with a mayor and council would have its own police force, not just a sheriff.
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 ★