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 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.
Revealing mistake: As the camera looks at Schultz driving the car, even though he's moving in the seat, you can see through the back glass the car isn't moving at all.
Revealing mistake: The film is flipped as the swastikas on the Gestapo uniforms of Hogan's men are reversed.
Revealing mistake: As the scene opens, the camera starts on a shot of the guard tower's roof. As it pans left and down into the yard, over the hill on the left side of the shot you can see a modern crane structure and the corner of a building in the distance.
Revealing mistake: When the guys are by the half-track keeping Shultz busy, if you look just above and to the left of Shultz's head, you see some tall fencing at the top of the hill in the distance. From the set up, if appears to be a baseball field outside of the studio property.
Revealing mistake: When the men are in the yard during their exercise period playing football, there is a wide shot of the yard. The half-track is to the left of the screen with Shultz next to it. If you look above the barracks, the Desilu water tower and a large metal building, possibly a studio building, can be seen.
That's No Lady, That's My Spy - S6-E17
Revealing mistake: When the men are in ranks for roll call, it's snowing heavily. Given the pitch of the barracks' roofs, there shouldn't be any snow sticking. Therefore, if looked at closely, it can be seen that the "snow" on the roofs is painted in place.
Answer: It's a comedy, not a documentary.
stiiggy
Perhaps it was counterfeit. There are numerous episodes where they deal in counterfeit monies.