Revealing mistake: As the building is being prepared for the upcoming event, and men are going in and out, as Shultz goes to report to Klink, look past him and the roof behind him. You can see the studio water tower in the distance.
Anchors Aweigh, Men of Stalag 13 - S1-E16
Factual error: When Shultz is standing at the top of the ramp with a crate marked "hors d'oeuvres", talking with Carter and Lebeau, if you look to the right of Shultz's head (camera's left) you can see the Desilu Studios water tower.
Factual error: When the men are lined up to take the strongboxes of gold to switch with bricks, each man in line easily hefts and tosses them to the next man. Gold bricks weigh over 27.5 pounds (12.4kg) apiece. If there 10 bricks per box (going by the size of the boxes), then that comes to 275 pounds per box, plus the weight of the box, which these guys are tossing around without a problem.
Continuity mistake: When explaining the "experiment" Lebeau has going, the multi-chambered tube is on the left (from the camera's POV) and the long tube with the coil is on the right. As the men up to leave after Carter comes in, the tubes are reversed.
Continuity mistake: Toward the end of the episode, Hogan turns Shultz around, grabs one of the grenades Shultz is carrying, and hands it off. The one grabbed was closest to Shultz's left side. A few moments later, Shultz turns his back briefly to the camera; there is now a space between the grenades, as if Hogan grabbed the middle one.
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.
Continuity mistake: In the first episode, when seen from the inside, the door to the outside opens from the left. In the rest of the series the door opens from the right.
Continuity mistake: After the POWs cut the stairs outside Col. Klink's office, Sgt. Schultz walks down them. There is a guard standing to his right. After a switch to show the POWs, when the camera goes back to the stairs, Col. Klink walks out and falls when the stairs collapse. The guard is missing without making any motion to move before. When everybody rushes to Col.Klink, the guard runs in from the left also.
Continuity mistake: When a German Major is in Col Hogan's quarters he is wearing black leather gloves. He raises his hand to remove his hat (with gloves). Next scene he is lowering his hat with bare hands. (00:02:10)
Kommandant of the Year - S1-E3
Continuity mistake: At least twice while the characters are under the large tarp around the rocket, there are at least three control panels visible. After the rocket fires and they show the general walking toward the people, behind him is the rocket trailer with only the tarp on it and no control panels.
Other mistake: In the movie, as the jeep comes up to Byron Buckles' plane, the jeep rolls through previous tracks from previous takes.
Factual error: During the whole show, the iconic Prussian helmet, the Pickelhaube, is present on Klink's desk. If Klink was a flier in WWI as he often hints, that is wrong. The German Reich's air corps didn't wear such helmets but had peaked caps instead.
Other mistake: When the General arrives at Camp 13 and is greeted by Klink, he notices Hogan and ask Klink who he is. Klink only says he's the Senior POW, the General sends his Aide to get Hogan. The Aide addresses Hogan by name, but Klink never said Hogan's name. (00:07:40)
Color the Luftwaffe Red - S4-E8
Factual error: The medal Newkirk steals from the German officer in the pub is a Knight's Cross of the Iron Cross with Oak Leaves and Swords. There were a total of 148 presentations, most of them 1943-45. By 1942 (where the series is apparently set), less than 25 had been presented. That Newkirk should actually stumble across a wearer by pure chance is highly unlikely, that the wearer should actually "never miss it" as Newkirk states, is plainly impossible. Being the fourth highest ranking military decoration of the Wehrmacht, it would have been missed almost immediately - if not by the wearer himself, then by his fellow officers. (00:22:35)
Character mistake: After Le Beau is questioned, Schultz is told to take him back to his cell. Schultz calls "About face! Forward march!" The "about face" is wrong. The door that Le Beau goes out is on his right, therefore the command should have been "right face."
Will the Blue Baron Strike Again? - S4-E12
Continuity mistake: At the airfield, Carter and Newkirk go to move, Carter steps left, and falls into the water. Newkirk takes a step, and leaps into the water, losing his hat, and trying to make it look like Carter pulled him, but you can see him looking to the way he falls. When the camera angle changes, Carter is splashing about, and Newkirk walks up to him from the left without having gotten out from where he fell. And his hat is on, despite losing it from jumping in.
Other mistake: Usually, the picture at the podium has the microphone "bug" for Hogan, and it's blatantly obvious, except to the Germans. This time, there is no bug, but an extra picture that the boys can take the eyes out of and listen in.
Revealing mistake: Every time they go to destroy a truck convoy, you can see that it is a miniature set with model trucks blown up, and it is a re-used shot every time. Same goes for the trains that get blown up.
Continuity mistake: Carter and Hogan are in Klink's outer office when Hogan takes a piece of paper off Carter and folds it into a square. Klink arrives and grabs the paper which has now unfolded to a rectangle. (00:09:10)
Visible crew/equipment: When Major Hochstetter's car arrives at Stalag 13, it drives towards the camera. The shadow of a crewman's hand raised to stop the car is visible on the ground. (00:16:40)