Continuity mistake: At the beginning of the show, Barney and Andy are sitting inside a 1964 Ford patrol car. When they are shown up close inside, you can tell it is not the likeness of the same car. The back glass windows look more like a 1960 model possibly. It is definitely not a 1964.
Revealing mistake: Barney and Mr Weaver scuffle in the dark. When Andy enters the store he turns on the light, but the light switch is still in the off position.
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 ★