Toward the end of the film, Jennings says that the place name Megiddo derives from the term Armageddon. Actually, it is the other way around - "Armageddon" is a bastardization of "Har Megiddo", which, in Hebrew, means simply "mountain of Megiddo". According to Revelation 16:16, this would be the site of the last battle in history.
When the photographer takes a picture of the priest the second time, in the park, the picture is taken at a distance if many yards against a background of trees and tall shrubbery. The developed photograph shows the priest in close-up with no vegetation at all.
In the first scene when Robert Thorne is being driven through Rome, the time is specified as 6.00AM and the date is June 6th. The sun rises in Rome at 5.30am at that time of year, which would mean it was reasonably light outside, but Robert is being driven in the dark.
The process for revealing a photo goes like this: Revealer, Water, Fixer and Water. When Jennings is revealing the picture, he takes it out of the revealer and exposes it to light, without the picture being submerged in fixer. A picture that has not been in fixer will start blackening instantly by the light. He treated the photo as though the whole process had been completed.
When the young nanny hangs herself, the window is seen breaking in three consecutive shots (outside long, inside, outside medium); it breaks in a different way in each shot (top half, bottom half, bottom 3/4).
In the final scene at the graveyard the President and his wife can be seen standing shoulder to shoulder as they are approached by the Secret Serviceman. The next camera shot, a split second later, they are standing apart as Damien has now been stood between them, holding their hands.
When Jennings is killed, you can see the hydraulic rubber belt flinging the plate glass off the back of the loading truck towards the manikin upon its supposed impact against the log Jennings was kneeling behind.