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.
Factual error: After the raven attacks journalist Joan Hart, pecking her eyes out, she blindly staggers into the highway and is run down by a Mack tractor-trailer. As the truck locks up its brakes and strikes her, we see Joan Hart levitate straight up into the air, arc completely over the truck's massive front-end (even over the cab of the truck), and finally impact the top of the freight trailer, which is about 13 feet in height. More than merely absurd-looking, this sequence utterly defies Newtonian physics. From her standing position at ground level, Joan Hart should have been instantly pulverized on impact and launched many meters down the road in the same direction the truck is traveling.
Visible crew/equipment: When the boys are leaving the home in the beginning you can see a boom mic moving over the hood of the car.
Continuity mistake: When Mark dies his body falls to the ground falling forward. After Damien screams and goes over to him his body is now lying across the path.
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.
Factual error: When the shipping container is opened none of the items are secured so they would've been broken during shipping, making it impossible to view the wall anyway.
Revealing mistake: When Joan Hart is knocked down by the truck she is replaced by an obvious dummy, it is more obvious when the dummy hits the ground.