The costumes for Rear Window were designed by Edith Head, one of the most famous costume designers in Hollywood history. Hitchcock used her a lot (in Notorious, To Catch a Thief, Vertigo, and The Birds, among other films), and her fantastic clothes were all over Hollywood in the '50s and '60s. Here's a picture of her. If she looks familiar, that's no mistake. She served as the inspiration for Edna Mode in the 2004 Pixar movie The Incredibles. (Source)

Hitchcock chose Raymond Burr to play the villainous Thorwald because of his resemblance to David O. Selznick, the famous producer Hitch worked with on three films. The two famously battled over control of the films, and the result, according to Hitchcock scholars, was the end of the Hollywood era where producers held all of the cards. The murderous Thorwald was an "in yo' face" from Hitchcock to Selznick. (Source)

Hitchcock directed the actors in the apartments via earpieces that remotely transmitted his direction. During the scene where the couple sleeping on the fire escape has to drag their mattress back inside during a rainstorm, Hitch deliberately radioed each of them different instructions on how to drag the mattress. The result was a lot of confusion and bickering, which Hitchcock loved and kept in the film. (Source)