In the original 1976 film, Father Brennan said he was present during Damien's birth, that he was born in a hospital, and Brennan is said to have a 666 mark on his thigh suggesting he is also part of the cult. In this film, none of those things seem to be true. He appears to be trying to bring down the cult and does not appear to be present when Damien is born, nor did Damien appear to be born in a hospital.
The film takes place in June 1971; however, in the original The Omen (1976), the birth of the child took place one year earlier, in 1970. This is established when Ambassador Thorn and Jennings open the tomb of Maria Scianna and her child: the date of death on the tombstone is VI VI MCMLXX (6/6/1970 in Roman numerals)
At the scene in the disco the song Daddy Cool from Boney M. is played. Thats a factual mistake: The song was released in 1976 - four years later.
The Latin in the birth scene is inaccurate - "Femina" is Latin for woman, the correct word for girl is "Puella"
When Margaret goes to Father Brennan's apartment, he must unlock a well-bolted door. The top lock (a door chain) is fitted incorrectly allowing the chain to easily slip out the hole.
The disco bar scene is a disaster. Many of the costumes were from after 1971 when the film is set. Four of the five songs that are heard in the disco came out years after 1971. It is also hard to believe that a Catholic novitiate as devout as Margaret would ever go to such a place, especially dressed as she was, regardless of whether she had taken her vows yet.
The song "Daddy Cool" by the group Boney M. is heard in the disco scene. This song was released in 1976 and the film is set in 1971.
During the disco/bar scene, the second song heard playing is "Domani" by Raffaella Carra. The song was not released until 1980, but the film is set in 1971.
The fashion used by the supporting characters, as well as the extras in the film, do not belong to the early seventies, but to the middle of that decade.
During the disco scene, where Margaret goes to dance with Paulo, the song playing is "I've Got To Use My Imagination" by Gladys Knight and the Pips. The song was not released until 1973, but the film is set in 1971.
When Margaret and Luz go to the disco together, the first song heard playing is "Rumore" by Italian singer Raffaella Carra. The song was not released until 1974, though the film is set in 1971.
The explanation that a cult within the Catholic church wants to bring about the coming of the Antichrist in order to counter increasing secularism in the world is a flimsy one. Even if it was an attempt to restore the power the church once had over people by making them believe in God again, which Father Brennan says is the case. But, if they believed in their own teachings, bringing about the Antichrist would simply bring about the end of the world.