Star Faye Grant would later become famous when she exposed her former husband Stephen Collins as a sex-predator; she played tapes from their marriage counseling sessions where he admitted to exposing himself to children. Many called this move (sending private and confidential tapes from a therapy session) vindictive and underhanded on her part. Other people applauded her bravery in alerting the public to a sexual predator.
A "fetus papyraceus" is also known as being a "vanishing twin". The Wikipedia website states: "A vanishing twin, also known as fetal resorption, is a fetus in a multi-gestation pregnancy which dies in utero and is then partially or completely reabsorbed by the twin. The occurrence of this phenomenon is sometimes referred to as twin embolisation syndrome or vanishing twin syndrome (VTS), since the 1980s when twin pregnancies were made visible early on by means of ultrasound. Occasionally, rather than being completely reabsorbed, the dead fetus will be compressed by its growing twin to a flattened, parchment-like state known as fetus papyraceus."
While Damien did not become aware that he was the Antichrist until he discovered it for himself, Delia was apparently aware of her identity as the granddaughter of Satan and the protector of the new Antichrist.
It is never revealed who the mother of Delia and Alexander is but it's probable that it is Kate Reynolds from the Final Conflict (1981), and that Delia and Alexander were conceived as a result of Kate's night with Damien.
The film was pretty much across the board critically slammed, hated by the critics and not a ratings success, this drove the last nail in the coffin of the Omen franchise. The franchise would not be resurrected again until 2006 with the Omen remake [See: The Omen (2006)].