The First Omen was very nearly given an NC-17 rating--largely for the disturbing birthing sequence, but after resubmitting the film to the MPA four times--with the problematic scene still included with every resubmission--the MPA eventually relented when it was cut down from its original 13 seconds to its final form receiving an R rating.
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.
Ralph Ineson's character, Father Brennan, is a slightly younger version of the same role played by Patrick Troughton in The Omen (1976). Throughton was 55 at the filming, while Ineson was 52.
The movie is set in 1971, just prior to the events of the prologue of The Omen (1976) (although the prologue of The Omen actually took place in 1970, as seen by the gravestones in the original film)