When Catherine lights the letters on fire, they are at first away from her dress, but in the next shot they are burning on top of her dress.
When Jules, Jim, and Albert are sitting on the grass sharing stories about the war, the order of the three characters repeatedly changes between shots. Note that this is actually a goof on the Criterion Region 1 disc, and the Tartan Region 2 DVD, in which the film is reversed left/right. It does not occur in other DVD releases of this film, including the Fox/Lorber Region 1 release.
When Jim has to return to Paris after his long stay, he jumps onto a train where the locomotive pulls two passenger cars and a cargo carriage (in that order) out of the station. After the cut to a longer aerial shot, it is pulling a cargo carriage and three passenger cars.
When Jim arrives by train at Jim and Catherine's house in Germany, a shot from the air depicts a French (SNCF) train. When the train arrives in the station in the next shot, the SNCF logo is hidden from sight.
Around the 35th minute, a train is shown. It is supposed to be just after WWI (the girl, Sabine, is very young), but the train is marked SNCF. The SNCF was founded in 1937... Many years afterwards.
When Jim recites La Marseillaise, the sound doesn't quite match up to the way that his lips are moving.