When the blood is flowing from the statue's heart and Father Fermoyle addresses the worshiping crowd, the length of the flow on the statue is inconsistent between cuts going from nearly all the way down the statue to being shown at midway down the statue and returning to be all the way down the statue.
When Stephen returns to America to help Father Gillis and the racial crisis in Georgia, his brother Frank mentions that he is regularly performing in a speakeasy. However, at this point the story has moved ahead to 1934. The repeal of the nineteenth amendment had occurred in December of 1933, ending Prohibition. Therefore, speakeasies would have been a thing of the past.
At 2:29:15 in the film, an Austrian banker -a suicide- is buried in hallowed ground, a scene set in the early-1940's. Until 1962 such burials were strictly forbidden for suicides.
All along the movie, we see, leading to St Peter's square, the Via della Conciliazione and its palazzi, built for the Holy Year of 1950, under the pontificate of Pius XII, whose election Cardinal Fermoyle is supposed to take part at the very end of the movie.
After the screen card indicates that the year is now 1934, Stephen's brother Frank informs him that he is singing in a speakeasy. However, Prohibition officially ended in 1933 after the 21st Amendment had repealed the 18th. Thus, speakeasies should have been a thing of the past in 1934.
As Father Stephen Fermoyle (Tom Tryon) crosses the street to enter a Boston pawn shop (approximately 00:52), the shadows of an arc light and grip stand are seen on the pavement during a sweeping pan.
Toward the end of the movie, Bishop Fermoyle says that the first American bishop was the brother of a signer of the Declaration of Independence. In reality, the first American bishop, John Carroll, was the cousin of Charles Carroll, who signed the Declaration of Independence. Bishop Carroll's brother, Daniel Carroll, signed the Constitution.