Factual error: When Cary Grant is attacked by the crop duster, he is supposed to be between Chicago and Indianapolis. Unfortunately, northwest Indiana looks nothing like this. The scene in the movie has miles and miles of treeless landscape. Even in the flattest farmlands of Indiana, there are many visible groves of trees.
Factual error: In New York, a newspaper headline reads, MANHUNT ON FOR UN KILLER, with a smaller headline below reading "Nixon promises West will remain in Berlin". The next night Eva Marie Saint reads the crop-duster plane story in the Chicago Sun-Times. Since the Sun-Times was a morning paper and the accident occurred in the afternoon, she must have been reading the following morning's edition. But a smaller headline underneath carries the same story: "Nixon promises West will remain in Berlin"; two days later, it's old news.
Factual error: At the end the couple are supposed to be returning from Rapid City, SD, to New York by train. The last shot shows a locomotive of the Southern Pacific Railroad. The word "Pacific" on the two locomotives has been covered over (but not on the baggage and four passenger cars visible before fade-to-black). The consist is a mix of SP paint schemes, all of which identify the railroad regardless of names on the side. It would have been easy for them to obtain SP train equipment in LA, but it seems odd that they would have bothered to modify the railroad name on the locomotives, particularly since it changes the name to the name of a another real railroad that didn't serve the US north of Cincinnati and Washington D.C.: the Southern Railway.
Factual error: The address of the art auction is 1212 N. Michigan. Michigan Avenue only extends north to the 900 block.
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.
Factual error: In the final escape scene on top of Mt Rushmore 3 of the Presidents are shown, but in the wrong order. They are shown in the movie, left to right, Washington, Roosevelt and then Jefferson. On Mt Rushmore in real life, left to right, it's Washington, Jefferson, Roosevelt and Lincoln.