When Hogan and the others first see the silent airplane, it is a twin-engined model. However, when it it on the ground, it is a single-engined aircraft.
The wide shot of the noiseless plane flying overhead does not match the plane that landed nearby. The tail sections are different.
When Hogan hides the briefcase under the mattress, he places it with the handle at the end of the bunk. When Schultz discovers it, the handle is at the side of the bunk (turned 90 degrees).
When Kintzler is showing the plane to the Luftwaffe Generals, from the behind shot Burkhalter is leaning on the car door. When they go to a front shot showing the Generals- Burkhalter is no where to be seen. Then reappears on the behind shot. Update: Klink is also in the behind shot, next to the car and in line with the two generals in the middle seat of the car (the driver is in the front seat, and two other generals are in the back seat), so Klink should have been in front of the leftmost general in the front shot (the one in the back seat, to the left of the screen) - but Klink is also gone from the front shot.
There is supposedly an airstrip nearby where the plane landed. There is no mention in future episodes of an airstrip this close to camp.
When they are dismantling the engine to discover the secret of the silent engine, Hogan says that it is because the fuel is vaporized in a series of baffle chambers. This makes no sense, as the noise from an internal combustion engine comes from the detonation of the fuel in the cylinders, not from vaporizing the fuel (which occurs in the carburetor).
When Sgt. Schultz bets 4 Mark, he uses 4 single bills. These did not exist. The smallest Reichsmark bill had a value of 5 Mark.
The two-way radio they used to bug Klink's office was called a 'walkie-talkie' - at the time, they were called 'handie talkies'.
Assuming the walkie-talkies used in the bugging scheme are standard SCR-536 models, they would weigh about 5 pounds each. So, the one placed in the soft-sided briefcase would have caused it to hang down much more than it does.
When the plane with the silent engine is seen flying it is clearly a low-wing plane with two vertical stabilizers (tails). When the heroes go to steal the engine it is a high-wing plane with a single vertical stabilizer.
When Newkirk is painting Klink's name on the briefcase, his paintbrush is black, but the letters on the briefcase are white. In addition, with all the handling of the briefcase immediately following, the supposedly freshly painted letters aren't at all smudged.
Newkirk is drawing a portrait of Carter, the drawing has the part in Carter's hair on the right but the real part is on the left.
When LeBeau is playing the harmonica behind Schultz, the sound of the instrument is clearly being dubbed in. Mouth movements not matching the sound.
In some scenes, there is a reflection of the production lighting in Klink's monocle. In one scene, two production lights are reflecting in the monocle.
After the plane landed at a nearby airstrip, it was conveniently parked within feet of the outside tunnel entrance.
At night, Hogan tries to camouflage himself, yet he is wearing his Air Force hat with the shiny brass insignia on it. Also, he is wearing his customary jacket with the shiny silver eagles on the shoulders.
On a couple of occasions, Carter, who is not married, is clearly wearing a wedding ring.
When Schultz places the briefcase on the chair in Klink's office, Burkhalter is sitting in such a way that he is almost facing the door. The movement of the door opening and Schultz putting the briefcase on the chair would have been noticed immediately.