Some cast members in studio records/casting call lists did not appear or were not identifiable in the movie. These were (with their character names, if any): Lloyd Ingraham (Woodrow Wilson), Alex Melesh (Headwaiter), Eddie Acuff (Taxi driver) and Mary Forbes.
The machine offers a variety of 2,372 entirely original codes. That would give an inquisitive outsider 2,371 chances of being wrong, even if he had the machine to work with.
Student: Does this machine take the place of former code books?
Instructor: Oh, not at all.
The part in Joel McCrea's hair keeps changing from right to left during the film.