Continuity mistake: In the beginning once McClane and Matthew have escaped the apartment, and are going through the alleyway, when John gets in the car and throws it in reverse look to the left of the screen. The back driver's side window is rolled down about 2-3 inches. The remaining camera shots during the escape show the window being rolled all the way up.
Continuity mistake: When confronted at Woodlawn, the bad guy is looking at McClane or Ferrel depending on the angle. (01:33:00)
Continuity mistake: When Detective Maclean is trying to convince Matt to go with him, Matt tries to open a window, so he can escape, but the window won't open. Later, after all the gunfire, both men escape through the now-working window.
Continuity mistake: When the hacker pulls up the F-35s schematic, it is shown with 10 missiles outline in red, 3 on each wing, and 4 internally. When the F-35 is shown on screen, it has no weapons mounted on the wings. (01:47:20 - 01:47:50)
