Continuity mistake: John's face is all bloody after he rolls from the car and "kills a helicopter with a car". The blood on his face constantly changes during the shots. Sometimes there is blood all over his face, sometimes there is quite a bit less. Sometimes he has blood streaming from the cut on his nose, sometimes there is nothing on his nose. The blood changes back and forth, so it's not just him wiping the blood away from his face (and his hands are by his sides during all the shots).
Continuity mistake: When McClane and Farrell are fired upon during the escort to DHS, Agent Johnson is killed and slumps against the steering wheel. In the next shot he is alive, looking back through the car's rear windshield, and jolts forward with the car's impact with the car in front of them.
Continuity mistake: In the scene where McClane rebuffs Ferrell for thinking it would be cool to do the firesale, you can see pipes for firehoses right behind McClane. When the shot changes to a long alley shot, the pipes are a good ten feet away, but when it reverts back to a closeup, the pipes are back to right behind McClane.