Character mistake: In the first scene of the show, Andy, Opie and the mayor are on a pier fishing a lake. They are casting with deep sea reels. If you've ever tried casting with a deep sea reel, it doesn't work out well. You can see there no equipment on the poles.
Character mistake: When Andy and Barney are looking through the yearbook, Barny's middle name is Milton. But Barney says many times throughout the series that his name is Bernard P. Fife.
Character mistake: Mr Darling says there are only 5 strings on the guitar he hands to Andy. You can see all 6 strings when the camera shows Andy playing Dooley.
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.