Plot hole: Since they took down the telephone network, it would have been impossible for Justin Long to even be speaking to the emergency response woman for the car, much less send a signal to start the car up.
Suggested correction: Is it possible this is a satellite phone call akin to Onstar?
No, the BMW system requires a cell signal to work, which was taken down earlier in the movie.
Plot hole: The hackers cause a massive traffic jam by manipulating the street lights. Yet, only minutes later, the streets are conveniently empty when McClane is being chased by the chopper. Sure, one or two streets were secured by police, but the chase scene goes through many more streets. (00:23:15 - 00:38:55)
Plot hole: When Lucy is stuck in the elevator, and they re-activate the elevator and turn all the lights on, Lucy should have been able to push the buttons and get to the floor. She did not have to wait for someone to rescue her.
Plot hole: When in the tunnel, McClane gets back into the cop car and leaves Farrell, he drives very quickly. After the helicopter blows up, it is only a few seconds before Farrell finds McClane. Even running at his top speed, Farrell could not have reached McClane's position so quickly. (00:42:00)
Plot hole: After McClane, agent Johnson, and Ferrell leave in the police car, Agent Johnson radios another agent to have DC police clear a path for them. Then on Gabriel's screen it says they have a voice match to Farrell. The problem is Farrell never said a word, so how would they have a voice match to him? Without the voice match they never should have found them.
Suggested correction: The agent says "Ferrell" over the radio which in turn gets picked up as a name match on Gabriel's screen as they were scanning for anyone using that key word. Not Ferrell's actual voice but anyone mentioning his name over the radio.
If it was just looking for anyone saying the word Farrell it would have been a "voice" match. A voice match implies but they got a match to Farrell's voice.
In this context it is a match on the name "Farrell" that was spoken, hence it is a "voice match." It's clunky but still works grammatically.
Plot hole: Why would Gabriel use a government vehicle at the end of the film that could be easily tracked and give his position away?
Suggested correction: Gabriel using a Government tracked van isn't really a plot hole. The plot hole should actually be how Bowman was able to track it considering Gabriel turned off the satellites. No satellites means no GPS tracking.