After Alex talks to Martin on flight to America, Alex leaves and goes to the stairs (going to upper deck, e.g. like 747). When the plane is landing, the view of the landing plane is one with a single-level passenger compartment.
When Martin is holding the photo of Anthony and they show a close-up of the photo, it is the same close-up with Philomena's thumb in it that we saw earlier, not a man's thumb.
When Martin enters the car at the monastery he has a messenger bag on his shoulder, but inside the car the bag isn't there.
When Martin calls his editor in London it is obviously evening in Washington. In UK it would be 5 hours later, in the middle of the night. Not the time for people to be at work.
When Martin wants to show a photo to Philomena, he zooms in on Michael Hess and people around him in a way that the journalists are not visible on the screen. But then Philomena finds Martin among the journalists on the screen.
Martin tells Philomena that in the United States, agencies are legally required to open their records to the birth mother on demand. This is not universally true. Laws vary by state and county, and in many areas the records are sealed and require a court order to open.
Anthony/Michael was born on July 5, with the movie based on Philomena's search for him on starting on his 50th birthday. The scenes on both sides of the Atlantic, however, show autumn colors.
Dame Judi Dench was 79 at the time this movie was released. If her character had been a teen mother, her age would have been mid to late 60s, 50 years later.
Stephen said that Anthony was snatched at birth, but he was several years old.
When the phone rings in Martin's Washington, D.C. hotel room, the ringtone is typical UK, not US: two short rings, which repeat. "Filming Locations" indicate that interior hotel scenes were filmed at the London Marriott Hotel. The sound editor should have changed ringtone.
The church in the end scene is obviously in England. Even if a church of this appearance existed in Ireland it would not be in Catholic ownership as all pre-reformation churches were given to the Anglicans. They should have found a credible church while filming in Ireland.
When Martin is viewing the website about Michael's life, the word "whilst" is used. This page most likely was written by Americans. Americans don't say "whilst"; they say "while."
Though the film appears to be set in 2004, the red Mazda MX-5 in which Pete Olsson arrives at his house is a third-generation model, not launched until 2005.
Michael's birth-date is shown as July 5, 1952 and he is seen to have died on August 15, 1995. Martin tells his editor that he died 8 years ago, which would make the movie's present year 2003; however, Philomena mentioned it would have been Michael's 50th birthday, which should make the present year in the movie 2002, not 2003.
The Ford Escape which Pete drives in the US in 2004 is a second-generation model from 2007.
The BMW hire car in Ireland has Republic of Ireland registration plates and a Northern Ireland tax disc.