Factual error: The priest says that St. John saw the number 666 in his vision, but it was actually 999 inverted. St. John wouldn't read modern Arabic numerals like we do, it would be Roman numerals. The number 666 would actually be DCLXVI. (01:05:40)
Factual error: As the subway trains are disconnecting, Arnold fires a 203 grenade launcher at Satan, knocking him back onto the other train. A 40mm grenade doesn't arm itself until about 15-25 meters, so unless Satan jumped extremely far, the round would not have detonated. (01:43:05)
Factual error: Arnold's wife and daughter are shot once each. There should not be blood on all four walls of the room.
Answer: The Vatican is aware of the birth, somewhere in the world, of Christine (though not knowing her identity at the time), and the Satanists are present at her birth and know that she is "the one." It's safe to assume that the Vatican, and the Catholic Church in general, has spies/informants in the Satanists' society, and were able, in the intervening 20 years between Christine's birth and the events of the film, to track her down to New York and send Aquinas there (the fact that he was sent by the Vatican is established).