Other mistake: When Andy and Helen are in the squad car alone after going to the movies with Gloria, both car doors are closed, but in the closeups from outside both sides of the car, note that both triangular vent windows are missing and we can see the doors' rubber seal - both doors are open for these closeups.
Visible crew/equipment: When Gloria and Frank drive off at the end, just as the camera zooms in on Andy and Helen, the shadow of the moving boom mic is visible at the top, left side of the screen.
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.