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: Cary's position was close to Eva and he almost kissed her, but then his position is farther away when he asks, "Shall I?" Also, in the kissing scene, when Cary is shown he is kissing her near an open door, but then they are against the wall again. (00:53:40)
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.
Continuity mistake: At Prairie Stop 21, after the second man arrives, shots on Thornhill show that his left arm is bent (the sleeve is folded), but the wide shot on both of them shows his arms at his sides. (01:09:45)
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.
Suggested correction: The fact that you can see the far shore of the "Great lake" tells me this isn't Ontario, Erie, or Michigan. I always assumed it must be the Finger Lakes, but I'm not familiar with the topography there. Just an assumption based on the knowing the Great Lakes and knowing that's not what was out the window.
Revealing mistake: Right after Eve "shoots" Roger and meets up with him and The Professor, some of the trees wobble as the ambulance drives past them. (01:46:20)
Continuity mistake: When Eva Marie Saint is going out to the aeroplane near the end of the film, it is dark as they walk away from the house, but by the time they reach the plane it is suddenly daylight.
Continuity mistake: When Thornhill is talking to the maid in Kaplan's hotel room, right after she identifies him as Kaplan, his arm changes from bent over his stomach to straight at his side. (00:29:45)
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)
Character mistake: When Cary Grant holds up a picture in the hotel room, he says, "he's assembling the General Assembly today" instead of addressing the General Assembly. (00:30:00)
Continuity mistake: While drinking in the train Thornhill's hand is grabbing the glass or not, depending on the shot. The position of the glass to his face also changes.
Continuity mistake: When Thornhill is about to be run over by the truck his jacket is covered in dust. When he falls on the ground it's spotless, only to appear dirty a shot later.
Continuity mistake: When the truck is about to run Thornhill over, skidmarks running along the road appear/disappear randomly between shots.
Continuity mistake: When the plane crashes against the truck its wipers face the left side. A shot later they are facing the right side.
Continuity mistake: When the opening credits roll-in stating that the events are fictitious, there is a shot of a woman in blue exiting a building. When the credits end after Hitchcock's cameo, the same shot is re-used though this time from a couple of seconds earlier.
Visible crew/equipment: Right before Thornhill gets shot by Eve, he's talking to Vandamm at the table. The camera moves backward. You can see its shadow on Thornhill's arm.
Visible crew/equipment: When Thornhill exits the phone booth 6 stage lights are reflected on the glass door.
Continuity mistake: When Thornhill is served a Martini in the train, check the toothpick and you'll see it keeps moving around between shots.