Stupidity: The first time they see the bad guy in the Land Rover, Morgan has him in his sights but can't shoot, as he doesn't want to kill him. Clearly, the obvious thing to do is to shoot the car tires, but he doesn't and lets him drive off.
Suggested correction: Shooting out car tires is not an actual effective strategy to get a vehicle to stop. A 9mm bullet simply doesn't cause enough damage to a tire to get it to go flat immediately. It causes similar damage as running over a nail. It is a movie cliche, similar to using a gun to shoot out a lock or a rope, it just doesn't happen in real life.
Other mistake: The ambulance that picks up Jeremy Piven is from Santa Barbara, CA when the movie takes place in North Carolina. (01:13:23)
Suggested correction: While the movie does take place in North Carolina, this scene occurs when they have followed the "Gentlemen Caller" into the woods near LA.
Plot hole: Given that police departments, the FBI, and the CIA do intense screening of potential candidates how did Casanova slip between the cracks? He's clever but surely somebody would've noticed something.
Suggested correction: In truth, there have been plenty of real life corrupt cops, and even cops that were secretly serial killers. If they managed to slip through the cracks, then it's not outside of the realm of possibility that Casanova was able to, too. So this is definitely not a mistake.
