When Gregory Peck walks out of the cabin, he is unshaven, but when he's seen outside the cabin, he's clean-shaven.
When the boy is watching Nick ride his horse and then quickly runs down the hill to get closer, he is not breathing hard at all when he reaches his stopping point.
A young boy spends almost the entire film walking across the mountains for days, then, when he puts his feet up, the bottoms of his moccasins are neither soiled nor worn but look brand new.
The movie was set and filmed in the Mojave Desert, yet in an early scene at an Army camp, the still night air is filled with the sound of crickets and frogs. This would be fine had the camp been in or near an oasis, but it clearly was not. With no wind, there should have been no sound at all from outside the camp.
Eva Marie Saint is clearly wearing mascara and lipstick when the tribe is captured. In several scenes, it is obvious that her fingernails are both manicured and polished which is absolutely wrong for the part she plays (i.e., "Sarah Carver").
In the finale as Sam is trying to stalk Salvaje, it makes absolutely no sense that he has not removed his noisy spurs.