Continuity mistake: His suit changes colour as he is running from the aeroplane. First blue, then brown, then back to blue.
Continuity mistake: When Cary Grant and Eva Marie Saint are riding in the dinner car on the train, there are several instances where the landscape/view as seen from their window repeats itself. Keep an eye out for a bridge they never get any closer to, and a section of tall iron work near the tracks they keep passing over and over.
Continuity mistake: The top and back of Mount Rushmore looks nothing like they portray it in the final scenes of the film. This is a mountain, and they would need climbing equipment to get to the top of the mountain. Also there are no trees at the top, and the is a vault at the top of the mountain, behind the monuments. This vault was originally planned to be used as a museum, but Congress withdrew funding because of World War II, and the museum was never completed.
Continuity mistake: In the scene where Cary Grant runs out of the hotel and jumps into a waiting cab, the two bad guys giving chase immediately jump in the next cab and should be the very next vehicle right behind Cary Grant's. But when Cary Grant looks behind him through the cab window to see if he's being followed, the bad guy's cab has disappeared. We get a clear line of sight all the way back to the hotel and the car is not there. Instead we see a third cab pulling into the space they just left.
Continuity mistake: When Cary Grant's character, Roger Thornhill arrives at the UN building in search of George Kaplan we see his shadow fall onto the door of the cab, as if the sun is behind him. But when you look at the pedestrians on the sidewalk, their shadow falls in the opposite direction. Simple mistake to make when using 3 point lighting in a studio environment to produce a rear projection process shot.
Factual error: In the drunk driving scene when Thornhill was on his way to New York City from the Townsend mansion, there are no high cliff roads along the ocean in any route he may have taken. There are some cliffs in the Montauk area but that's over 100 miles away in the opposite direction and there are no high winding roads.
Factual error: The 20th Century Limited train, where Grant and Saint first meet, is supposed to be heading west in the afternoon, past the Great Lakes which should be on the right side of the train, but the lakes are visible through the windows on the left, so the views were shot heading east, and the supposed lowering late afternoon sun would in fact be the sun soon after sunrise.
Audio problem: When Thornhill and Kendall reunite after the shooting, they are obviously on a soundstage and not on location in the wilderness. There is absolutely no background noise, which is impossible in the outdoors: leaves rustling, birds calling, water trickling, wind gusting, etc. prevent the complete silence depicted by the movie. The quality of the actors' voices also sounds like indoors rather than an open space. (01:46:30)