When Gerard pockets his service pay after signing discharge papers, there are two female actors in the background holding files. But on the next immediate cut, there is now only one actor and she is looking through a cabinet drawer.
When Gerard is in the British passport office, there is a photo of Winston Churchill on a wall behind a clerk. But on the following cut, the picture has changed position.
In the window of the Bern insurance company, the German word for insurance, "Versicherungen" is misspelled "Vesicherungen".
The transporter bridge can be seen through the window of the Marseilles police officer's office. The bridge was partially destroyed in 1944 and the rest fell down in 1945.
When Madeleine Jarnac enters her apartment she turns on the light indicating that the apartment is dark. However before she turns on the light, you could see her shadow which was caused by the production lighting setup.
Gerard isn't willing to wait for the investigation so he can a passport to travel to France legally. So he uses a small boat to sneak into France. But it's never explained how he got to and traveled to Argentina and back to Switzerland in Europe with no papers (passport).
When Gerard arrives in Argentina he is approached by a Professional Guide named Incza that knows his occupation. Gerard does not know Incza but nevertheless Incza goes uninvited to see Gerard at his hotel room and Gerard lets him in. He even undresses and takes a shower in the presence of this stranger. Gerard never questions Incza or acts as if anything is out of the ordinary. The whole interaction does not make any sense in the context of the film, the Gerard character or the real world.
After the maid notices that the mailman did not pick up the forwarded letter to Madeleine Jarnac, she comes out of the house and looks toward Gerard. He in turn looks back toward her and then reads the letter. Nothing, however, became of this; the maid did not yell or call the police therefore there was no purpose in the maid noticing that the letter wasn't picked up. The film also never explained this.
When Gerard goes to break into the Bar Fortuna, he uses his Luger pistol to break the lock on the sliding window. He first removes the magazine, but does not clear the chamber. He then smashes the lock, and replaces the magazine. Only then does he operate the toggle link and a shell can be heard hitting the sidewalk. In short, he smashed the lock with the pistol still loaded.