Character mistake: Barney complains about Andy escorting the Apricot Queen around Mayberry many years prior. Barney had hoped to be her escort. He remembers the date, telling Andy it was "June 23, 1952, a Saturday afternoon." June 23, 1952, was a Monday.
A Black Day for Mayberry - S4-E7
Character mistake: When Opie comes in at the beginning of the episode and asks where Andy is, the exchange ends with Barney asking "Something you want to see him about?" and Opie replying "No, I'll wait," which makes no sense in context. It would have made more sense if Barney had asked "Do you want to leave him a message?"
My Fair Ernest T. Bass - S4-E17
Character mistake: During the party at Mrs. Wiley's, Ernest Bass' girlfriend is called "Ramona." At the end of the show, Ernest T keeps calling her "Romina".
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.