Visible crew/equipment: After the boys meet Flip Conroy and talk about the football team, when they all disperse and Opie starts walking away the T-mark is visible on the ground.
Floyd, the Gay Deceiver - S3-E9
Continuity mistake: At the start, when Floyd and Andy walk into the barbershop, in the exterior shot Floyd's white barber jacket is on a hanger hanging from the coat tree that has a finial at the top of its pole, but in the next interior shot that jacket is hanging directly on the coat tree's hook, the hanger has vanished, and that finial has disappeared as well.
The Darlings Are Coming - S3-E25
Visible crew/equipment: During the scene where the Darling's truck has overheated, Andy walks up from the back of the truck. As he comes into view you can see what appears to be a microphone cord hanging out from under his pants leg.
Visible crew/equipment: After Aunt Bee plants the seeds of suspicion in Andy's mind about the shoe salesman, when Andy and Barney cross the street the reflection of the moving boom mic is visible on their squad's windshield, just as Andy walks off to the hotel.
Visible crew/equipment: When the men have the misconception that Wilbur is a TV show talent scout, while they're at the barber shop talking about it, just as Floyd moves his legs to get up from the barber chair we can see the white T-mark at Jason's feet.
The Taylors in Hollywood - S6-E8
Visible crew/equipment: After the studio's security guard tells Andy they're filming on stage 40, when it cuts to the Taylors walking onto the set we can see two chalk T-marks on the floor (one in front of Andy's feet). (00:13:00)
Continuity mistake: When Gomer drops the gun from the roof it lands on the ground directly in front of Andy and Barney, who are standing on the sidewalk beside the courthouse, but the area where they're standing looks different between the overhead shots and closeups, and their shadows change as well. Additionally, the gun lands with its handle to the left, but in the wideshot the gun is lying the opposite way, with its handle to the right.
Continuity mistake: At the end, when Andy walks in on Barney showing Gomer how to draw his gun, Gomer draws his gun out of the holster which sends it flying behind him, and in the closeup the bookcase glass shatters, but in the wideshot when they all turn to look the glass is still perfectly intact.
Continuity mistake: At the start, when Andy stops at Wally's station Gomer is telling Jason about his Trout bait, then someone pulls up behind Jason's car and they're bumper to bumper in the wideshot, but in the exterior shot facing Jason there's no car behind him, but that car is back again before he pulls away.
Opie's Group - S8-E9
Visible crew/equipment: After Aunt Bee asks Clara to speak to Opie, in the interior shot just as Clara walks into the house we can see the two tape marks on the floor, where Clara and Opie will stand.
Visible crew/equipment: After the squad car is hit from behind Andy rushes over to Goober, and a T-mark (it's a bit darker than the color of the dirt road) becomes visible on the ground (just as the woman gets out of her car) at the bottom of the screen, right behind Andy's feet. (00:01:25)
Other mistake: During the scenes at Goober's filling station we can see a few brand names covered. For example, the "Chew Mail Pouch Tobacco" wall thermometer sign has its brand name "Mail Pouch" covered with black tape, and all the yellow "Pennzoil" cans have half the letters of their brand name painted yellow, so all the cans read "en zo."
Opie's Group - S8-E9
Continuity mistake: While the Taylors are having dinner and talking about Opie's band, Opie has a filled dinner plate, salad plate, glass of milk, and flatware spread out on the table in front of him, but it all disappears in the shots facing Aunt Bee and Andy.
The Bazaar - S6-E5
Visible crew/equipment: After Andy shouts at Goober to get his pickup truck away from the courthouse, it cuts to Andy, Warren, and all the women in the courthouse, and we can see the chalk T-mark on the floor at Warren's feet.
Visible crew/equipment: While Aunt Bee, Andy, Barney, and Gomer are on the porch talking about the band, just as Andy says, "We're talking about gettin' up a band concert by tonight," the chalk T-mark is visible on the floor by Andy's feet. (00:12:25)
The Legend of Barney Fife - S6-E18
Continuity mistake: At the start of the episode, while Barney's in Andy's kitchen he's wearing a shirt with large distinctive designs, but when he and Andy walk into the courthouse Barney's shirt has completely different designs (though it's the same type of shirt). (00:01:00 - 00:04:00)
A Visit to Barney Fife - S7-E18
Continuity mistake: While Andy and Barney are sitting on the porch, Barney's clip-on striped bow tie is clipped on the opposite way (stripes flip) when Ma and her family get back from "shopping." (00:14:45)
Visible crew/equipment: At the start, just as Mr. Hampton walks into the office and pushes the door closed, we can see a crew member's hand reaching through the doorway to help close the door. (00:00:55)
The Gypsies - S6-E23
Continuity mistake: While Andy and the townsfolk are at the courthouse during the storm, when The Gypsies walk in the two men are wearing wet rain ponchos and the woman is wearing a striped serape, but then she's wearing a wet raincoat, and it switches yet again in following shots. (00:21:45)
The Cannon - S6-E11
Visible crew/equipment: After Warren accidentally fires The Cannon, in the following closeup of Andy commenting that he shot a station wagon, the shadow of the moving boom and mic is visible at the lower left corner of the screen. (00:22:05)
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.