Character mistake: As we know throughout this movie series, Michael's middle name is Audrey. However when the doctor is typing Michael's release form, he types his middle initial as "M".
Suggested correction: Michael's middle name is only mentioned in an additional scene that was added to the television version of the original Halloween. If going by the theatrical versions Michael's middle name was never known, so not really a mistake.
Doctors at a sanatorium would certainly know Michael's middle name. It's been on file for decades.
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).
Suggested correction: This presumes that a person can notice the difference between a fully-loaded pistol versus a pistol that is empty, which makes sense. However, it would be much more difficult for a person to tell that a gun is completely empty versus one that only has one or two bullets loaded. Since Gruber has no way of knowing his ruse didn't work, he doesn't believe McClane would have given him a completely empty gun. He obviously believes there is at the very least one bullet in the gun. He's not planning on getting into a shootout with McClane, he is just planning to threaten him and he certainly doesn't need a fully loaded gun to do that.
Suggested correction: It's easy to tell the different between the weight of a loaded vs. unloaded pistol, but given Hans had never held the pistol before, he had no way to compare the weight. Unless he regularly handled that particular model of pistol (unlikely, given his pistol is a completely different make and model) he would have no point of reference.
Character mistake: As the prosecuting DA finishes his statement about Kenneth Joyce to the Jury, he tampers with the Jury by assuring them they won't believe Joyce's witness testimony. And somehow the judge does not catch this or ignores it completely.
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.
Character mistake: When Nico comes out of the parking lot and gets caught by the police, right before he gets in the van and is patted down by the police officer, the police officer says, "she's clean", not "he's clean."
Character mistake: When Dr. Walker and Michelle are dancing at the club, the people around can't help but stare at the camera.