Deliberate mistake: The Messerschmitts have painted yellow fronts, this wasn't done by the Germans until after Dunkirk. Christopher Nolan has admitted doing this deliberately so the audience could tell the difference between the Spitfire and the Messerschmitt during the combat scenes.
Factual error: Robert McNamara is wearing a multi colored Polo shirt talking to Mrs. Graham in 1971. The Ralph Lauren Company did not make the shirts until 1972.
Factual error: When flying to France to have talks with the French premier a C47/Dakota is shown in the background intimating that it was the plane he came in. The C47 did not enter service with the RAF until after this period of the film with Lend Lease.
Suggested correction: The aircraft could just as easily be the civilian version, the DC-3 which first flew in 1935, and was pressed into RAF service and repainted.
The RAF did not requisition civilian DC3s or DC2s. It is well recorded that Churchill flew to France in May 1940 in a de Havilland DH.95 Flamingo. Only 16 were built - de Havilland cancelling DH.95 production to make more Tiger Moths desperately needed for pilot training. The DH.95's were cannibalised for spares, the last scrapped in 1953, so the film production company may be excused for their C-47 use. Though a Lockheed Lodestar may have been a closer simile.
Factual error: When Mark Felt and the FBI Director are in a car on the way to the Watergate hearings in 1972 or 1973, from the car window, you see the WW2 memorial, which was built in 2004.
Factual error: In a picture from the UN headquarters in New York in the year 2003 you see two German flags. The German Democrativ Republic hasn't existed since 1990. (01:16:04)
Revealing mistake: Back at his NAACP homebase, Marshall meets with the boss who is already sending him to deal with another case. In the close-up of the newspaper he's reading, check out between the actor's fingers. You can tell that half of the article, which begins in English, suddenly switches into Latin 'lorem ipsum' filler text. (00:06:20)
Factual error: The scene with Queen Victoria in Florence happens too early since it is supposed to happen in the spring of 1888 but Abdul Karim was not yet her official "Munshi", being appointed to that title in August of the same year.
Factual error: The accident takes place the night of July 18, 1969, and they show there being a full moon. That night the moon was actually waxing crescent with only 14% visible, and set at 10:27pm while the accident happened about 12:45am, so there was no moon in the sky anyway.
Continuity mistake: Man-seob smears some cream above his upper lip after a few smoke grenades are deployed. The amount of cream shown over his upper lip changes between shots.
Factual error: Since the movie was set in the 60s, David Senak couldn't have gotten in trouble for shooting the man running away. In the 60s, the police could legally shoot any criminal running away. This didn't change until Tennessee v. Garner in 1985.