Continuity mistake: When Edwards is teaching Hunt the alphabet, whenever he turns it around or you see it from another angle, the upper and lower case changes.
Other mistake: The Indian woman has a bikini tan line above her rear in the bathing scene. Bikinis didn't exist in the 1800's.
Revealing mistake: When Chris is being hanged you can see the back of his jacket being pulled up from the harness.
Continuity mistake: When the Barber pulls Chris' tooth, the pliers change from the time he puts them in his mouth and when the tooth is pulled. Once opening sideways they then open vertically.
Continuity mistake: When Mathew Perry moves the telescope to show Chris the naked indian woman, he moves it to the left, yet the view through it shows moving to the right.
Continuity mistake: Near the end of the film, Hunt threatens and chases away Guy Fontenot, who runs off. Note that here, he is wearing his head scarf thing. A couple of shots later, Guy reappears behind Hidalgo, once again wearing his helmet. He then disappears for the rest of the movie.
Factual error: When Chris Farley is climbing up the side of the mountain to return the bird egg, you see the bottom of his moccasins and they appear to be made of a ribbed (for traction) material. Back then, they would have been made from animal hides and the bottoms would have been smooth not ribbed.
Revealing mistake: When Mathew is looking at the stars and his telescope falls, the wire that is attached to the telescope is visible.
Other mistake: When Bidwell comes back from being mauled by the bear, he has a wooden "crutch". When you see him up close the crutch is sawed or finely cut on the top. He was lost in the woods so I don't think he could find one of those.
Factual error: In the final scene, when Mr. Hunt is planting the flag in the beach, we see the original 13 star pattern, and another larger star in the middle. However, in 1804, there where already 17 states in the union, so the flag should have 17 stars.