Continuity mistake: When Ray Winstone takes his pill with whiskey while talking to Mel Gibson, he takes a swig of the drink and knocks the pill back, leaving some alcohol in the glass. When we cut to a wide shot his glass is completely empty.
Other mistake: After Craven shoots the driver of the car that took his car door off, you can see that there is no gas tank underneath the car.
Continuity mistake: In the scene after Craven talks to the Senator, the vehicles beside his police vehicle change from the shot showing him enter the car to the next angle showing his car leave its spot.
Factual error: When Craven is pulling over the car in the tunnel exiting the city, the vehicle pulls over in a completely different part of the city. (00:58:40)
Revealing mistake: When Mel Gibson is fighting the boyfriend, he flips the table at him, and you can see that it's a double. There are other instances where you can spot the double, but this one is so close and clear. (00:26:55)
Revealing mistake: In the scene in the beginning of the movie when Mel Gibson's daughter gets shot and he's cradling her dead body, when they zoom out her hand is moving. Her fingers move quite a bit when Mel pulls her into his arms.
Chosen answer: Possibly from getting his daughter's blood on him, when he accepted a drink from the Northmoor executive, or from handling his daughter's radioactive belongings. Given the depth of the coverup, they may have even anticipated that she'd come to him and broken into his house and poisoned him before the story even began.
Captain Defenestrator