Character mistake: An unloaded automatic pistol is much lighter and balanced differently than a loaded one. When McClane hands "Bill Clay" (Gruber) the empty pistol, a terrorist of Gruber's credentials should pick up on the odd balance (I notice that difference, and I very rarely even pick up a gun).
Character mistake: The psychologist on the TV news is talking about the "Helsinki syndrome", the news anchor comments that Helsinki is in Sweden (before being corrected). There is no such thing as a Helsinki syndrome. However there is a thing called the "Stockholm syndrome". This refers to an actual hostage situation in 1973 in Stockholm, Sweden, when bank robbers held the staff in a bank hostage for several days. During the time in the vault, the hostage and the bank robbers developed a strange kind of friendship, and this is called "the Stockholm syndrome".