Question: Beginning with the "Convicts at Large" episode in season 3, full width window boxes appear at the bottom of both front windows on the inside of the Sheriff's Office. Prior to this episode, they did not exist. Window boxes are often used to display decorative plants but I don't see any plants. And if they were supposed to partially block the background, the blinds were long enough to accomplish that. I find it hard to believe that the producers would spend additional money (for material and labor) for something that seems to serve no purpose. So why were they added?
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.
Answer: I suspect these were common, as to block the wind from blowing the blinds and papers on the desk.
Question: Was this show cancelled or simply ended?
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.