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 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.
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.