In several interior scenes, Rock Hudson's hairstyle and sideburns are drastically shorter than in the rest of the film. This seems to give credence to the rumors of studio interference and the necessity of re-shoots.
In the "Cafe Can Can" scene the World War I American pilots are said to belong to an "Eagle Squadron" but that term was only used for Americans flying with the RAF in World War II.
The planes' guns (both Allied and German) fire too quickly for the bullets to pass between the planes' propellers.
When the telephone rings in the film, it is with the British double ring rather than the single ring that would be heard in France.
Public address announcements are heard when Lily Smith and Colonel Kurt Von Ruger enter the train station. While public address systems were invented in the US in 1915, they weren't commercially available until the 1920s - several years after the movie's 1918 setting.
Rock Hudson as American pilot William Larrabee is far too old for a WW1 pilot. Aircraft's were a recent invention and pilots for all sides were in their early 20's and not their mid-40s as Rock Hudson was at the time of the filming and most pilots had a very brief career and short life expectancy.