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.
Factual error: In the beginning of the movie after the scene where John watches his daughter go inside, he is called on his police radio. The gentleman on the other end is in fact talking to him on a land-line telephone and not a radio, but from Johns end you hear the mic being keyed on and off. Police radios cannot make or place telephone calls and vice-versa. (00:06:45 - 00:07:50)
Suggested correction: Although very unpopular and very unlikely to have been installed in a Police car, some radios can indeed ring landline telephones. They were known as "Mobile Radio Telephones" but they tended to be extremely unreliable.
Revealing mistake: Airbags are made out of a super strong fabric material with heavy weaving. There's no way McClane would be able to tear it. You can see the texture difference between McClane's fake airbag and the real passenger side airbag.
Suggested correction: Incorrect, the driver's airbag is designed in such a way it can be ripped out. This is a safety feature to be used in a life or death situation if the car is still driveable. For instance, if someone rams you off the road and the airbag deploys, you can rip it off and continue driving to try and escape the assailant.
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.
Continuity mistake: John M is driving to the Eastern electricity station and chatting. The view out of his window shows him driving past the same distant hill at least three times. Also the speed is faster out of the passenger's side than the driver's.
Factual error: They crash their BMW, and Doloris comes on in the On-Star system. On-Star has never been available in BMW vehicles, as it is a wholly-owned subsidiary of General Motors. BMW does offer a similar service called BMW Assist, but this was not available in any BMW model at the time of this movie.
Suggested correction: Where did you get OnStar from? It was "RoadAssist", OnStar is not mentioned at any point. Nor do they crash the BMW, Matt whacks it with a bin.
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.