Not long into the film, Reeve, at the Vatican, is asked by his Boston bishop, who actually seems to be dressed as a cardinal, Robert Prosky to follow him.He does, and is hat less. They stroll in the "Vatican" gardens, which appear to be the Villa Borghese gardens, When Reeve's told an army buddy is there to see him, he runs off. They jeep to a mafia stronghold of black market stockpiles. Reeve gets out of the jeep, suddenly with his wide brim black hat.
When the officers pick up the nuns in the rain, the jeep they are in has no side windows or doors. However when Reeve turns around to chat with the nuns in the back seat, his seat clearly has a window (still none in back). When they let the nuns out the magic door and window are once again gone.
At Fr. Flaherty's ordination, the presiding bishop speaks of "several of the young priests we have today ordained" enlisting as military chaplains. The shot then shows him and his fellow ordinands listening to the bishop's address, but all of them are wearing wearing their stoles over their left shoulders. This is the style appropriate to deacons; if they had been ordained, their stoles should be hanging around their necks.
At the end of his Requiem Mass in the field, Father Flaherty says "Requiescat in pace." The Mass, however, was clearly celebrated (as would be expected in a war zone) for more than one person (as indicated by plural pronouns in a previous prayer). In that case, the correct verb form would be "Requiescant" and not "Requiescat."