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.
Continuity mistake: While Thornhill and his mother are investigating Kaplan's hotel room, he decides to try on one of the man's suits from the closet to see if he and Kaplan are similar in stature. He tries on a navy or dark colored suit coat and then holds the pants up against himself to check the length. In the close up of the trousers, they are now a light gray in color. The camera returns to a full shot and, once again, he has the darker trousers in his hands. You can also see the light gray suit in the closet behind him. (00:31:25)
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.
Continuity mistake: While Roger and Eve converse before dinner on the train, Roger's glass mysteriously changes places several times. When shot from behind, he's holding the glass; from the front, it's on the table.
Continuity mistake: Near the beginning of the film, as Thornhill has arrived at The Plaza and is opening the door of the taxi to exit it; visible through the rear window is a red and white Ford taxi, parked behind Thornhill's taxi. Instantaneously, in the next shot taken from the sidewalk, he is shown completing his exit from the cab. Now however, there is a light colored Dodge taxi cab parked directly behind them. (00:04:20)
Other mistake: The second bus in the scene before the crop duster has no license plate.
Continuity mistake: In the last scene before Chicago the train is going through the tunnel at Breakneck Pass north of Cold Spring NY. When they're going back home at the end of the movie theoretically they should be going the same way but they're not. The final tunnel shot in North by Northwest is the Southern Pacific railroad tunnel between Santa Susana and Chatsworth California. (01:00:10 - 02:16:05)
Plot hole: When Eve is being led out to the airplane, she bolts when two shots are fired from inside the house (presumably Anna firing at Thornhill, not realizing that the gun was loaded with blanks). Moments later, she jumps into a car driven by Thornhill, and they escape together. There is no way Thornhill could have gotten there that fast, given that he was in the house only seconds earlier.
Continuity mistake: On the patio outside the restaurant at Mt. Rushmore the professor goes inside first. His shadow falls upward to the right, there is no glare on the upper windows and no building shadow on the ground. Thornhill walks in seconds later and his shadow falls downwards to the left, there is a strong glare on the windows and the building casting a shadow on the ground.