Trivia: In the scene when Cary Grant is going up the steps to the UN, Alfred Hitchcock shot it from a rug truck across the street. He wasn't allowed to shoot the front of the UN. If you look closely, you can see a security guard in the left corner.
Trivia: Alfred Hitchcock's cameo comes at the end of the opening credits. He can be seen missing the bus.
Trivia: Cary Grant was born on January 18th, 1904, and the actress playing his mother, Jessie Royce Landis, was born on November 25th, 1896, making her just seven years older than Cary. According to commentary on the DVD, it was thought that casting Landis as Cary Grant's mother would make Cary look young enough to be a believable love interest for Eva Marie Saint.
Trivia: After Eva Marie Saint snatches the sculpture containing the microfilm from James Mason, Cary Grant remarks, "I see you got the pumpkin." This was evidently a reference to the Alger Hiss case, in which Whitaker Chambers testified that Hiss had given him government secrets that had been hidden in a scooped out pumpkin in a pumpkin patch in Hiss' back yard.
Trivia: In the auction gallery, Cary Grant says to Eva Marie Saint, whom he sees with the spies for the first time, "The three of you together: here's a picture only Charles Addams could draw." This referred to a New Yorker cartoonist who specialized in macabre and grotesque characters. The reference would probably have been lost to Italian viewers, but the dubber did his homework, and the translation was, "The three of you together: just like something out of Dracula and Frankenstein."
Trivia: Thornhill is looking up at the Mount Rushmore sculptures, using the fixed, standing binoculars for tourists, and he exclaims: "I don't like the way Teddy Roosevelt is looking at me." The thing is, Theodore Roosevelt, the third from left to right, is the only one of the four heads to be looking as much away from him as could possibly be. I wonder why the screenwriter, Ernest Lehman, made this particular choice? Perhaps he was having a joke on the perceived ignorance of the contemporary cinema-going public at the time. Either that, or it was just sloppy writing. My guess is he just asked some underling: "Who are the four presidents represented on Mount Rushmore?", and then picked one at random.
Answer: More than likely, they felt that Roger would be dead and they would not be found out. The fact that he survives their DUI plot and returns to the house with the police only serves to makes him look more suspicious and guilty. It's to move the plot along, nothing more.
ChiChi
The bigger plot hole is, if Van Dam really believes Roger is Kaplan, why would he think that Roger would bring the police and go through the trouble of preparing "Mrs. Kaplan" to make the police think he's crazy? If Roger really was a spy, he doesn't need help from the police and would have just disappeared instead of retracing his steps. So if Van Dam anticipated the actions taken by Roger, he must believe at some level that Roger is telling the truth and would have looked deeper into it.