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: Mac's cousin says that even if Nick wasn't a cop, he'd have to hate Mac's guts. He says that Mac wears a Rolex and Nick wears a Timex - not true. Nick is wearing a Rolex, also.