Other mistake: After the scene where the building explodes when the gas was rerouted to the station, there will be a shot of the main bad guy staring at the computer screen saying the connection failed. On one of the two connection lost screens, it says, "connection faild", this is not how you spell "failed". (01:16:45)
Other mistake: In the scene in which McClane and Farrell are in the car on the way to the Eastern Hub, the shots alternate between looking at McClane then looking at Farrell. When the stars are in profile there is visible through the subject's car window the landscape passing by, but the same hill appears outside each window. (01:00:55)
Other mistake: When the lights in the tunnel are switched off, you see that the cars that have been directed into the tunnel have their lights off. When you enter a tunnel, you are required by law to turn on your lights despite the lights in the tunnel. Sure, one or two drivers might ignore this obligation, but the whole avalanche of cars?