Factual error: The movie takes place in Chicago, except for one scene that is supposed to be in New York City (when Damien's uncle visits the priest). Two problems. First, as the cab pulls up to the church where the priest is, it goes past a housing project. Anyone who knows public housing construction in New York and Chicago knows that building is in Chicago. Second, when they go out to a trainyard, you can clearly see the Hancock Tower in the background. Of course, that building is in Chicago, not New York.
Revealing mistake: This scene takes place just outside the Thorn mansion in a snowy wooded area. Mark confronts Damien about being the Antichrist. Damien says yes and to join him. Mark declines, and then drops dead. In an extreme close-up, Damien yells out "Nooo." If you pause on his close-up, you can see dental work. Fillings or caps, whatever it is. He is supposed to be the Devil's son. He has never been sick or injured (mentioned in The Omen), and is immune to the chemical accident in this film, but oral bacteria? Secondly, even if his teeth can be vulnerable like ours, Damien was written as a 13 year old boy. That's a bit early for that kind of dental work.