Plane at the beginning of the movie changes from white to light green one. Also numbers on plane or the plane model don't match either.
When Karl is proposing a toast in honor of the family reunited at last (1h 01'), we can see Julio successively in the mirror and in close-up. In the mirror he has a glass in his left hand, but in close-ups the glass is in his right hand. The left-right hand images alternates three times.
In the scene where the German army parades through Paris (June 1940) they're marching under the Triumphal Arch and past the Tomb of the Unknown Soldier (this is indicated in the scene's opening shot with the eternal flame on the tomb). In fact, the Germans refrained from marching through the Arch, as did de Gaulle and the Free French in 1944. The German HQ wanted to avoid stirring up revulsion and hatred, and no parade at all has marched there since the Unknown Soldier was put to rest in 1920. They have all passed beside the Arch (part of the symbolism of the Tomb is a wish for "no more wars").
Although the film in set in the late 1930s, the costumes and hairstyles of the women are in very much in the early 1960s styles.