Audio problem: Just as McClane and Farrell are about to leave the Eastern Power Hub, Farrell goes on a long rant and his mouth does not match the words he is saying. [In the unrated version of the film, the rant concurs with Will's mouth movements, but the mistake is valid for the regular version.]
Audio problem: During the final chase scene when McClane takes control of the semi truck, you can hear the truck continuing to shift gears even though McClane is not completely in the driver's seat and nowhere close to the clutch or shifter.
Audio problem: After the terrorist in the helicopter opens fire on John and Matthew, a policeman yells something about backup into his radio. What he's saying doesn't match up with his mouth. (00:37:45)
Audio problem: As McClane attempts to escape from the car in the lift shaft, a henchman shoots at him. As McClane hides between the seats, he cries, "Motherf**ker!" However, McClane's lips aren't moving. ('Unrated'/'Ultimate Action Edition' version only).
Audio problem: When McClane and Ferral arrive at Woodlawn, Ferral says something about the cooling towers being on the lower floors. As he does, his mouth doesn't move at all. Granted his mouth is blocked for most of it, but you can see a bit of his mouth at points and it's not moving. (01:30:15)