Near the beginning, when the couple are in the asylum in the present day, the woman is reading aloud the history of Briarcliff. The information she is reading from states Briarcliff's most famous resident was Bloody Face. This is an error since Bloody Face was the psychiatrist, Dr. Oliver Thredson, not a resident.
When Monsignor Timothy Howard makes the sign of the cross, he does it backwards. It should be forehead, heart, left shoulder, then right shoulder. He consistently does it backwards.