Man's Best Friend Is Not His Dog - S4-E6
Revealing mistake: As Schultz holds Newkirk's hat during the search, you can see "Dawson" written on the inside band. This was to insure that Richard Dawson (Newkirk) always had the right wardrobe pieces.
Anchors Aweigh, Men of Stalag 13 - S1-E16
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: During the main part of the plot, the guys are putting dynamite on each truck in the convoy as they fuel up at Stalag 13. It is supposed to be dark, (hence the reason the boys wear black) but there are shadows as if it were day. It's impossible for the driver in the following truck and the guard in The Tower to miss seeing the boys as they go back and forth to plant charges.
Revealing mistake: When Schultz checks the barbed wire to see if it is fixed now, he noticeably wiggles the vertical wire, but only barely touches the horizontal one - because it is rigged to come apart, and will again if he handles it too roughly.
The Return of Major Bonacelli - S4-E25
Revealing mistake: When Hogan, Carter and Le Beau are talking to Schultz, you can see it is an overcast day. After Hochstetter comes in and the camera cuts to them talking about Bonacelli, it goes back to Hogan. You can now see that they are on a sound stage. The reasons are that the guard isn't moving in The Tower, the boys are well lit, and as Hogan and Le Beau go into the barracks, you can see differences in the painting of the sky on the back drop.
Sticky Wicket Newkirk - S3-E20
Revealing mistake: When Hochstetter goes to open the window in Klink's office after the explosion rocks the camp, look at the background. You can see the studio lighting shining on the matte painting of the camp yard.
Revealing mistake: When Le Beau holds up the gold painted brick and the "gold" brick, the ends reveal that they appear to be pieces of lumber. The ends seem to have grains consistent with lumber.
Movies Are Your Best Escape - S1-E8
Revealing mistake: When Schultz is talking to Hogan and Le Beau, the guard outside walks past. As he does, you can see three shadows from him revealing the studio lighting, rather than him really being outside.
The Battle of Stalag 13 - S2-E5
Revealing mistake: When the scene transitions from Klink and Hogan to a night shot outside of the barracks, you can see palm trees above the roof line. Not normal for the area that's supposed to be represented.
Revealing mistake: In the close ups of Maj. Zolle, it can be seen that the spectacles that he has on have no lenses.
Everybody Loves a Snowman - S3-E14
Revealing mistake: As the sink with the fake tunnel is prepared, just before Newkirk goes over to set things up, you can see movement through a crack in the door. It's Schultz, Hochstetter, and Klink, waiting their cue to enter.
The Flame Grows Higher - S1-E31
Revealing mistake: As Hogan, Le Beau, and Newkirk help Schultz up the slope to the "forest fire", there is lumber stacked across a low spot in the top of the bank and covered with "snow" and grass. Probably meant as a path.
Revealing mistake: As Klink steps off the porch of his office, in the long shot you can tell it is his stunt double.
To Russia Without Love - S6-E18
Revealing mistake: As the motorcycle and the side car split apart and drive around independently, you can see that the side car has been given two extra wheels, and some other stuff underneath as well that's not present on regular Wehrmacht BMW sidecars - probably a remote control of sorts. Also, the motorcycle Schultz rides has training wheels mounted in the shot where the side car comes off.
The 43rd, a Moving Story - S1-E23
Revealing mistake: As Carter and Newkirk sit by the wall catching their breath, a seam can be seen running vertically where two wall sections meet behind them.
The Kamikazes Are Coming - S6-E20
Revealing mistake: As the rocket blasts out of the recreation hall, the guide wires for the model are visible.
Revealing mistake: In the close ups, Professor Bauer's spectacles do not have lenses.
Revealing mistake: As the truck passes Carter and Newkirk, it's easy to tell they're hiding behind tarp-covered boxes rather than the greenery or rocks around them.
The Witness - S4-E23
Revealing mistake: As Schultz comes in the barracks door, there is a sliver of the studio background visible by the door jamb above his head.
Hogan and the Lady Doctor - S2-E20
Revealing mistake: As the truck pulls into the laboratory yard, the buildings of the city surrounding the studio backlot are seen.
Answer: It's a comedy, not a documentary.
stiiggy
Perhaps it was counterfeit. There are numerous episodes where they deal in counterfeit monies.