Andy's Old Girlfriend - S7-E20
Other mistake: At the cabin, when Andy and Alice are fixing breakfast at the kitchen counter, note the cereal box's brand name is covered (presumably painted), which is still recognizable as "Post Toasties." (Andy Griffith even did commercials for this specific cereal). (00:20:00)
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.