The Statue - S7-E23
Other mistake: At the end of the ceremony, when Aunt Bee finally unveils the life-size statue of Seth Taylor the prop jiggles (presumably it's plastic) back and forth on the base, even though we know it's carved out of a block of granite (stated by Howard earlier in the episode) by a stonemason. (00:05:00 - 00:22:55)
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.