Early in the film when Andrews is being followed by an investigator, he dodges him in a revolving door and walks into a store which has the name Hans Gruber on it. The villain in "Die Hard" is named Hans Gruber.
The movie opens with the first radio broadcast on Thanksgiving Day (1941). That would make it the date of November 20, 1941, just 17 days before the Japanese attack on Pearl Harbor, which thrust America into World War II.