Continuity mistake: When Tommy Lee Jones is reading the letter at the end of the movie, there is no signs of scar tissue on his hand, even tough he was cut there during his last fight with Benicio Del Toro.
Continuity mistake: When Benicio Del Toro is smashing into all the cars in the traffic jam, he does some major damage to the hood. Later, when investigators examine the abandoned car, the hood isn't bent or damaged at all. (01:01:00)
Continuity mistake: When Tommy Lee Jones is pursuing Benicio Del Toro under the city his shirt is wet almost all the way to his trousers, when he gets out of the hole its wet only on the top of his back. (01:14:49)
Continuity mistake: In the car chase scene, when Del Toro gets stuck in traffic, the car behind him stops just a few centimeters before. But when he decides to make room using his car, suddenly the car behind him is a few feet back, providing him with adequate space to drive in reverse. (00:57:10)
Factual error: Lots of liberties are taken with the geography of downtown Portland. For example, at one point Bonham is standing on a fountain looking around and, from his point of view, you see two MAX trains on a slope going past a parking lot. Those two points are about a mile apart and there is definitely not line of sight between them because most of downtown Portland is in the way. (01:07:40)
Continuity mistake: In the scene where they visit the girlfriend, Connie Nielsen has straightened her hair and changed her clothes. Suddenly they are in the girlfriend's attic looking at the safe that was just mentioned in a previous scene, and she has wet curly hair and a wet-shirt on. (00:52:45)
Revealing mistake: When the "light rail" vehicle is crossing the bridge, several shots reveal that it is not traveling on rails, but on a metal grating. This is most obvious after the police have stopped it. We see a bridge deck designed to carry cars & trucks (in fact, the police have just driven out on it) with strips of metal laid on the surface to simulate "rails". As others have observed, this was filmed on the wrong bridge; this makes it particularly obvious.
Factual error: When Hallam is trying to get on the train, the policeman says the subject is on the Hawthorne Bridge. The MAX light railway doesn't go over that bridge, it goes over the Steel Bridge. (01:10:00)
Continuity mistake: Near the end, when Tommy Lee Jones is hanging upside-down over the raging river, he pulls the wooden stake out of his leg. Blood starts gushing out and it leaves a pretty big hole in his thigh. Yet during his end fight with Del Toro, there is no marks on either thigh. (01:19:20)
Continuity mistake: In the short aerial shot of Hallam and Bonham climbing up the bridge there is no train on the bridge below them. (01:13:08)
Factual error: After Del Toro jumps into the (Willamette) river he floats/swims to the falls. In fact those falls are about 10 miles upstream from the point he jumps in.
Continuity mistake: As Aaron Hallam is leaving his girlfriend's house, he steals her car and races off as fast as possible. He easily passes LT Bonham. However a moment later LT is even with the car again. (00:58:30)
Continuity mistake: When Bonham follows Hallam down the river he is seen walking on the right bank. In the next shot he is walking on the left bank. (One could assume that he is going back and forth, but that would be very counterproductive on the hunt for someone who is swimming down a fast-flowing river). (01:12:00)
Continuity mistake: The colouring of the wolf's paw varies. When Tommy Lee Jones is tracking it, the paw is black. When the snare is being removed, it is pink with blood, and when the wolf is finally running away, the paw is white. (00:11:40)
Continuity mistake: When Tommy Lee Jones is pursuing Benicio Del Toro in the river, he gets very wet. In the next shot his hair and clothes are dry and clean.
Continuity mistake: The letter giving the Department of Defense jurisdiction over Hallam is dated March 5 2001. The caption about 12 minutes into the film ("Silver Falls, Oregon, 2003") sets it in 2003. (00:36:30)
Revealing mistake: In the shot where Jones is caught in a snare and is falling through the air towards the water, he comes to an unnatural stop at the end of his fall. He should have jerked when he came to the end of the rope. Instead, he came to a smooth, controlled stop with no jerking or bouncing. The stunt man was probably lowered with a crane.
Revealing mistake: In the scene where the two "deer" hunters are shooting at Del Toro, the report of the rifles is wrong. The report they use in the movie is for a semi-automatic weapon; you can hear the mechanical clang at the end. These hunters were shooting bolt action rifles.
Revealing mistake: When Aaron cuts the first deer hunter's cheek there is no slash but only a smear of 'blood'. (00:15:05)
Factual error: Near the end of the movie Del Toro was forging a knife with a fire he made out of twigs. It is not possible for that fire to heat the metal enough. A much hotter fire would be needed for smithing.