When the Department of Defense comes to take custody of Hallam, the letter used to give them jurisdiction, addressed to the FBI agent in charge, is dated "March 5th 2001." The events of the movie take place in 2003.
When Aaron steals the car from his family garage followed by the police chase, the car is majorly damaged as he flees. When we see car next it is dumped and the law enforcement are shown inspecting it, there is clearly no heavy front-end damage or damage whatsoever.
When Hallam quenches his new, red-hot knife in the stream, a jump cut is visible and the knife is no longer red-hot. Indeed, quenching steel in water takes considerably longer than the few seconds shown in the film (possibly why it was cut).
In the downtown Portland chase scene they show LT at "Ira Keller Fountain" (locally known as "4 Courts) looking about, peers over at a skate park...which is actually located at least a mile away, and across the river, under the Burnside Bridge.
When L.T is on top of the MAX train chasing Aaron, there is the "click-clack-click-clack" sound of a train, but when the camera shows the deck of the bridge behind and in front of the "train" you can see that there are no tracks (the Hawthorne Bridge carries cars, not trains). Tracks are only shown when the "train" makes an emergency stop before Aaron climbs up the bridge. Even then, the tracks are merely shiny strips of metal unevenly laid upon the bridge's metal grating, with no grooves for the wheels at all in the surface.
During Bonham's exploration of Irene's house, the timid cat on the bed upstairs is being restrained by a thin cable from underneath the cover. When the cat is panned into view, the cable is clearly seen being released, allowing the camera-shy feline to seek safety behind the pillow.
The wire used to pull the spike out of Bonham's leg when he's impaled on the cliff is seen as it whizzes by. The scene was first shot pulling the spike out, then played in reverse to achieve the desired effect.
When Bonham is first looking for Hallum after the two "sweepers" have been killed, he comes upon the remnants of the snare Hallum used. In the scene where the sweeper is caught by the snare, one can see it's made from 550 (parachute) cord. It is also 550 cord when Bonham tugs on it attached to the tree. However, the loop section of the snare that Bonham picks up with the stick is obviously constructed of wire.
In the final "tracking" scene where Bonham is searching the woods for Hallum, Bonham sets off a trap where two spiked logs come smashing together. In the scene his reaction is to step back out of the way. Immediately after, the scene cuts to him lunging on the ground. At this moment, one can look in the background and see a boulder with a rope tied around it instead.