The grizzly bear's paws change from brown to black and back to brown again in several scenes in the film.
When Kelly, Scotty, and Don are in the Jeep and see the hunters, the rear view mirror is not there. When they turn around to go back, the rear view mirror is there.
In the final showdown with the grizzly bear, Don is firing a left-handed bolt action rifle from the hip. When it is empty, he raises it to use as a club. The rifle he raises is a right-handed bolt action rifle.
Don offers his hunting rifle to Kelly, saying that the park ranger's "Army regular" is inferior to Don's .30-06. Kelly and the other rangers carry M1917 Enfields throughout the entire film, which are also .30-06 rifles.
In one shot of the watchtower's destruction by the grizzly bear, a rope can be seen flapping around, presumably the one that was used to pull the watchtower down when the scene was filmed.
When the body of Ranger Tom is shown after the watchtower's destruction by the grizzly bear, there is a movement in his neck
muscles.
When Kelly asks the helicopter pilot if he can get the helicopter any lower, the pilot responds "No. Too much of a downdraft today." He then lands it a few seconds later when they think that they have spotted the grizzly bear.
Whether you listen to the tagline of, or the characters in, the film, the grizzly bear is supposedly anywhere from 15 to 18 feet tall when standing up on its hind legs. But at the end of the film, when it is doing just that in order to attack the helicopter, it is clearly less than 10 feet tall.
Close up shots of the bears feet are shown several times during the movie, especially when it's walking. The feet that are shown are clearly from a Black Bear and not a Grizzly.
Camera shadows are visible in some scenes of the film.
A single grizzly bear would not have the strength that is needed to bring down a fire lookout tower.
Scotty describes the grizzly bear as cannibalistic after it kills and eats the bear cub that was set out as bait for it in order to both trap and kill it, but the cub in the film is an American black bear, which is a
completely separate species than the bear they are tracking.
The rangers discuss the fact that brown bears have been seen in the area, but grizzlies are not known to be in the area. Actually, the brown bear and the grizzly bear are two different common names for the same species of bear ("Ursus arctos"), with the first name mostly used in Europe and Asia (and formerly in North Africa, where it is now extinct) and the second one used in western North America.
Arthur Scott horribly mangles the scientific name of the grizzly bear the first time he says it; instead of "Ursus arctos horribilis", he says "Arctodus ursus horribilis".