Revealing mistake: Throughout the whole movie, bits of 'snow' stuck to various things in close up view (i.e. guns, hair, faces, clothing). Look closely at the snow, its quite obvious that they are actually little thin scraps of white plastic. Most evident is in McClane's hair when the platoon is about to move in on the church, the shot of him saying "You're not such an asshole, after all." (01:27:55)BillyBlake
Revealing mistake: When the army guy opens the door on the 747 to climb out onto the wing, the outside door handle does not move and looks painted on. When the second guy re-enters the plane and shuts the same door, there is no locking mechanism shown on the sides of the door; it simply pushes open.
Revealing mistake: When the soldier is lighting General Esperanza's cigar while Esperanza is still a prisoner in transport, the cigar is visibly already lit before the soldier's lighter brushes over the cigar. (00:24:30)