Visible crew/equipment: When Otis tries to escape from Aunt Bee's clutches by hiding in the laundry service van, just as Aunt Bee has the driver open the van's back doors we can see the reflection of the moving boom mic in the left window.
Visible crew/equipment: When the squad's siren gets stuck blaring, a crowd gathers around the squad with Andy, Barney and Rogers, and when the crowd disperses we can see at least three chalk T-marks on the ground.
Continuity mistake: When Andy and Barney catch up with the man who ran Fletch's truck off the road, the rearview mirror suddenly vanishes in the closeups that face the windshield on Bailey's car.
Visible crew/equipment: When the new manicurist tells Floyd that she works only on commission, she lifts the small table and moves it to the window, and we can see the actor's tape mark where she had just been standing.
Visible crew/equipment: At the start of the last scene, when Andy and Rogers walk out of the courthouse the reflection of a crew member is visible on the surface of the car, and as Rogers drives away we can see the reflection of the camera dolly on the car, and also the shadow of the boom mic on the ground.
Continuity mistake: When Otis begins his 24 hour sentence at Andy's house by staying in the guest room, Otis is wearing suspenders (braces) that are sewn together in the back in an X-shape, but when Otis leaves the guest room he's wearing entirely different style suspenders attached to his trousers.
Visible crew/equipment: When 'FBI Agent' Jenkins congratulates Andy and Barney on behalf of J. Edgar Hoover they're all standing near the door, but when it cuts to Jenkins turning around and they all walk over to the desk, we can see the two curved chalk lines on the floor where Jenkins' feet were positioned, as well as the curved chalk marks on the upper step where the mayor was standing.
Andy and the Woman Speeder - S2-E3
Continuity mistake: At the end, when Andy and Barney are standing beside the woman's car her rear-view mirror has vanished in the closeups, but when she drives off in the long shot the mirror has reappeared.
Continuity mistake: On the curb outside the courthouse there's a fire hydrant beside the pole, which not only changes its position on the sidewalk in different scenes, but it has also vanished at the end when Rogers drives away, as Barney crosses the street.
The Keeper of the Flame - S2-E14
Continuity mistake: When Andy holds Barney by the shoulders while congratulating him for an outstanding job of detective work, Andy holds his notebook in his left hand, but when it cuts to a different angle the notebook's suddenly in Andy's right hand.
Revealing mistake: The woman in the foreground, as the siren is stuck, is carrying a paper grocery sack from "Hollywood Ranch Market" which was located on Vine St and Fountain Ave in Hollywood, Los Angeles. (00:09:35)
Continuity mistake: When Barney disguises himself as an old woman, in the very first shot he's wearing a dress with lace and tiny flowers, but in all the following shots it's an entirely different dress with large groups of flowers. (00:17:40)
Visible crew/equipment: When Barney and Andy are waiting for Virgil to arrive, just as the bus pulls up and stops, the reflection of the boom pole/mic is visible on the windshield. (00:03:50)
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.