Dawson Casting: Both leads were older than their characters (actually it's not clear how old Roger is supposed to be, given that Cary Grant was in his mid-50s at the time).
Executive Meddling: The final shot of the film was to be the two leads climbing into be on their train and sharing a passionate kiss with "The End" superimposed over it, but The Hays Code objected, saying that it implied that the couple were going to have sex (which, let's face it, they probably were) and demanded it be changed. In classic Hitchcock form, he obliged and changed it to their traingoing into a tunnel.
Throw It In: An unintentional one. When Eve shoots Roger in the restaurant with the blanks, a child actor covers his ears before the gunshot happens. The take was still used, since aside from this, it was the best take.
As has often been noted, this is perhaps the closest we got to Hitchcock doing a James Bond film.
Legend has it that Hitchcock denied Jimmy Stewart the part of Thornhill because he thought he was too old for it... so instead he got Cary Grant, who was even older than Stewart. (Another theory is that the less-than-spectacular box office results for Vertigo caused a falling-out between Hitchcock and Stewart, hence no North by Northwest for the latter. ) Other actors considered or suggested for the role included Gregory Peck, William Holden, Frank Sinatra, and Dean Martin.
MGM wanted Cyd Charisse to play Eve Kendall (since she was under contract to the studio) and Cary Grant pushed for Sophia Loren (who he'd reportedly fallen for while working together on Houseboat). Hitchcock also considered Elizabeth Taylor before settling on Eva Marie Saint.
While the film was still in the early scripting stage, a scene taking place at an assembly line in Detroit was envisioned, where the camera would follow two men as they talked while a car was built behind them piece by piece... and at the end, one of the characters would open a door of the now-finished car and a corpse would fall out! Part of this sequence actually inspired one moment in Steven Spielberg's Minority Report.
Hitch himself noted that he wanted the climax to involve the heroes interacting with the faces on Mt. Rushmore, rather than just climbing around them. Specifically, he wanted Cary Grant to hide for a moment in one of the noses...and then have a sneezing fit. While the scene was filmed on a sound-stage using a model of the monument, so there was no risk of damage to the monument, there was a small public outcry during the film's production, which complained that climbing over the presidents' faces would be disrespectful, so Hitchcock had to agree that the movie would not have characters actually touch any of the faces.
Word of Gay: Martin Landau stated in interviews that he portrayed Vandamm's henchman Leonard as a closeted homosexual who was secretly jealous of Eve Kendall's relationship with his employer. In the scene where he revealed to Vandamm that Eve was secretly working for the Feds, he commented, "Call it my woman's intuition, if you will..."