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.
Revealing mistake: Towards the beginning of the movie, there are several shots of winter wilderness, one with a soaring eagle. If you look closely, you see that this particular eagle has tethers hanging off of its feet. This was not a bird found in nature. This was a trained bird brought in for this shot.
Plot hole: In one of the scenes where Jones and Del Toro are fighting hand to hand, Del Toro's knife is knocked into the bushes. They continue to fight until a point where Del Toro has gained the upper hand. Del Toro is on top of Jones, who is almost unconscious. Instead of finishing Jones off, Del Toro looks around for his knife. This doesn't make sense. Del Toro is a trained killer. He doesn't need a knife to kill Jones.
Plot hole: Near the start of the film Tommy Lee Jones tracks a wounded wolf through the woods and removes a snare from its leg. The problem with this is there is no way he could have just walked up to a wild animal start touching it without it attacking. Plus this is a wounded animal which as anyone who deals with animals can tell you makes them twice as dangerous.
Suggested correction: There are numerous real-world stories of people interacting with wounded wild animals without being attacked, so it's not a mistake for the movie to portray that happening here. Even if it were impossible, it would not by definition be a plot hole but a "factual error."
Other mistake: Once dropped off by the FBI helicopter Tommy Lee vomits and says he is afraid of heights and hates to fly. After Del Toro is detained and on the way to the tunnel, Tommy Lee claims he doesn't like flying and has an 8 hr drive back to his cabin. Next scene is him waiting in a airport presumably for a flight when he hears the report of the truck roll over.
