Factual error: Andy tells the hobo "that will be the 3:45 stopping for water", meaning its a steam locomotive, but by the time this episode was made railroads had long since switched to diesel.
Continuity mistake: At the beginning of the show, Andy notices a wanted poster on the office bulletin board and tells Barney that he had learned from news accounts that the wanted person had been captured. Barney removes the poster and places it in a file cabinet. The next day when Roger reports for duty, he and Barney are looking at the bulletin board and the wanted poster is back up.
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.