Revealing mistake: When the "Boat" is loaded on a "trailer", you can see that it has very little ground clearance. The wheels of the "trailer" actually are hidden behind the boards like on a parade wagon. The boat has no keel and no hull below its freeboard. Besides the question of how the boat got onto the trailer if it is practically built around it, there remains the question of how it is supposed to stay afloat without a keel or a bottom.
Revealing mistake: LeBeau hands Schultz the pan straight from the hot plate, but Schultz puts at least three fingers around it while eating without any apparent issues. Note that LeBeau earlier said the Crepe Suzette were "not quite ready yet" - or in other words, still cooking. (00:01:40)
Revealing mistake: When the boys set the trash can on fire in front of Klink's office, there is a problem with the trash. While the rest of the waste paper burns down there is one piece hanging over the top edge that doesn't burn, even being in the midst of the flames on that side.
Revealing mistake: Toward the end of the episode, a guard is watching Helga posing in a one piece bikini for Lebeau. As you look past him, you see only blue screen, no view of the surrounding property. Same when Hogan climbs up, you don't see the tops of buildings; you can tell it's on a soundstage.
Revealing mistake: After Hogan and the boys decide to get rid of Tillman, they "accidentally" set fire to the trash can on the Kommandant's porch. To that end they load up a bunch of trash that's been soaked in gas. Then Hogan tosses a lit match in it. The fire starts at the bottom, but all of gas soaked stuff, and the match, were at the top.
Revealing mistake: During the attack with crossbow, look closely at the arrow in the door. You hear the sound of the arrow hitting the door, then see the (now skewered) hat shaking on the arrow. If viewed closely, you see a black thread pulling on the arrow. Also, the arrow is almost straight before the break, then it is down at an angle when Shultz is called in.