Continuity mistake: McClane's shoulder holster disappears while fighting in the hanging truck in the elevator shaft. We can see he has the holster again (albeit a different kind) before the fight with the parkour guy.
Factual error: The Woodlawn shot of the hackers killing the security guards show mountains. There are no mountains in Woodlawn.
Continuity mistake: In the beginning once McClane and Matthew have escaped the apartment, and are going through the alleyway, when John gets in the car and throws it in reverse look to the left of the screen. The back driver's side window is rolled down about 2-3 inches. The remaining camera shots during the escape show the window being rolled all the way up.
Answer: The radio line mentioned the officer's name in the seconds after Gabriel's voice recognition picked up Farrell's name.