Barney Hosts a Summit Meeting - S8-E21
Visible crew/equipment: When Andy and Barney start to get into their car, the boom mic is reflected in the front window. (00:10:10)
Aunt Bee's Big Moment - S8-E23
Visible crew/equipment: After Aunt Bee's solo flight, just as the flight instructor walks over and gives Bee the papers as proof that she soloed, the large T-mark (rubber/plastic) is visible on the ground between Bee and the instructor.
Aunt Bee's Big Moment - S8-E23
Visible crew/equipment: After Aunt Bee tells Opie that she will solo the next day, when she sits in the chair to practice her flight maneuvers, the actor's tape mark is visible on the floor beside her feet.
The Wedding - S8-E26
Visible crew/equipment: The night of Howard's party, when the doorbell rings and Howard opens the door for Goober, we can see a crew member's head moving in and out of the shot at the right side of the screen.
Visible crew/equipment: After Andy gets the phone call about Sam's victory, when Sam is pushed to give a speech, a few white tape marks are visible on the floor near the fireplace.
Visible crew/equipment: After Emmett talks to to the diner owner about having the bus stop moved to double his diner business, when Emmett walks down the block, the reflection of the moving camera dolly is visible in the store window.
Visible crew/equipment: When Andy, Howard, and Goober walk into Emmett's shop to tell him that Sam's running for head of City Council, the shadow of the boom mic is moving on the wall behind them, at the top 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.