In at least four scenes, Herbert Kappler wears a black SS parade tunic instead of his usual office gray uniform. By 1943, when the film is set, the SS had completely phased the black SS tunic out of service and this uniform would not have been worn at even the most formal of functions.
When O'Flaherty spoke of his friends in Ireland being shot by the Black and Tan during "The Troubles", "The Troubles" weren't until late in the 20th century. Could've he meant during
the Irish War of Independence which happened in 1919-1921 during Hugh's lifetime (1898-1963) as when the Black & Tan shot many of his friends.
Kappler demands the Jewish community provide 100 pounds of gold. Germany had used the metric system since 1872 and the Italian states adopted metric in the 1860s. Neither used pounds before metric.
When any semi-automatic or full automatic weapon is fired, no empty shell casings are ejected.
The uniforms of most of the German troops lack any ribbons, badges, or other decorations. In reality, by mid-1944 many of these soldiers would have been battle veterans and would be wearing appropriate awards for that service. In addition, all uniforms and helmets are in clean, new condition, when in fact they should appear more worn.
When the priest, disguised as a Sturmbahnführer, is eluding his pursuers, the film is shown reversed; medal ribbons and collar insignia are on the wrong sides.
All the German vehicles appear to be new, and are unmarked except for the German cross and license plates. Real vehicles would look more worn, and would also display various numbers, unit codes, placards, etc. No two would look exactly alike.
When light reflects off of O'Flaherty's glasses, it's easy to see that they are made of flat glass with no prescription.
Gregory Peck is shown with white hair visiting a woman on a farm. In the next scene, his hair is black.
Hugh O'Flaherty is seen driving a right hand car. In Italy all cars are left hand drive even in Germany.
When Hugh O'Flaherty escapes from the Gestapo by disguising himself as a coal hauler, the SS officer who stops to question him wears rank insignia on the wrong side of the uniform collar.