Late in the movie, Ottway unfolds the letter, which then shows a large yellowish stain. Still later, he partially unfolds it before folding it into his wallet, and the stain is gone.
After the plane crash Ottway is seen covered in snow, but when he gets to the plane to see the survivors there is almost no snow on his sweater.
Just before Ottway stumbles into the wolf den, he is trudging alone holding Henrick's pack in his right hand. The angle cuts as he leans on a tree with his left hand, and it's clearly seen that he's holding the pack with that hand. Immediately after, it's in his right hand again.
Fastening a shotgun shell to a stick does not work as well as depicted. The Mythbusters demonstrated that the human arm simply can't thrust the stick hard enough to set off the shell.
When Ottway jumps into the rushing river to save a friend, he would not have been able to stand the freezing cold water for more than a minute. Afterwards, he lifts himself out of the water and continues his quest. Hypothermia would have killed him within minutes after leaving the water,
In the real world, wolves are after a meal, and can't afford to get hurt. They go for easy prey. They would not be harassing a dangerous pack of humans.
As said before, this movie takes no account of the real natural behavior of wolves, they would never 'hunt down' people, especially not a group of them and when there's fire around.
The opening scene has Ottway drinking in a bar. There are no bars on the North Slope Oil Fields, and no alcohol or weapons are allowed on the North Slope oil fields of Alaska. Workers caught with alcohol or weapons are terminated and permanently barred from employment on the "Slope". For safety and security reasons, all employees on the North Slope are closely monitored for behavior problems, even in transit to and from work.
During the final scene there is a flipped shot, which can be seen when Ottway's facial cut changes sides.
In the opening scene at the Bar you can see the woman in the background putting a yet refilled beer down a fake beer stapler with a fixed handle. She obviously had mistaken timing of her role.
Sitting around the fire, the snow on the men's beards would have melted.
Before setting off for the woods, Ottway searches through the plane wreckage and finds his rifle in its case, with the stock broken in two. He then discards the rifle. This is strange as, even with the stock broken and scope ruined, it would be possible to fire the rifle with reasonable accuracy at close range, certainly accurately enough to dispatch a number of wolves.
Unfortunately, planes are far more valuable than people. Whatever the reason that oil workers might not have been missed, their plane would have been (by its owners and the insurers) and a search for it would have been undertaken within HOURS of it not arriving at its destination. Additionally all US aircraft are required to have and maintain ELT (emergency location transmitters) which would help find the plane if it is lost. While this device might destroyed in the crash, this happens very few times when a plane has an accident in manner depicted in the film.
Henrick says his name his first name is Pete but later his first name is seen listed as David on his driver's license.