(at around 8 mins) When Maggie arrives in Rome, Cardinal Lawrence explains to her that there are ongoing riots between the Italian citizens, motivated, among other things, by students dissatisfied with the state and the Holy Church. This is historically accurate: after the social revolution of Paris in May 1968, this extended to other countries in Europe. In Italy it lasted from 1969 to the late 1980s, a period known in the country as the Years of Lead.
The movie is set in 1971, just prior to the events of the prologue of Das Omen (1976) (although the prologue of The Omen actually took place in 1970, as seen by the gravestones in the original film).
Ralph Ineson's character, Father Brennan, is a slightly younger version of the same role played by Patrick Troughton in Das Omen (1976). Throughton was 55 at the filming, while Ineson was 52.
Buildings in Villa Parisi and a farm in Procoio were used to portray the orphanage.
Cardinal Lawrence's hands appear to be partially paralyzed (ring and little fingers). This is not a character choice, actor Bill Nighy suffers from Dupuytren's Contracture. It's a hereditary condition that causes the ring and little fingers of each hand to be permanently bent inwards towards the palm.