According to the progressing seasons throughout the movie, the two gray colts attacked by the cougar in the beginning of the movie do not age as they should have done. This is evident as Spirit and Rain return to the herd together, and are greeted by the same two gray colts who remain weanlings as opposed to yearlings.
When Spirit is about to exit the train car and looks at the camp, the same shot with the mounted officer crossing the path is shown twice.
When Spirit is returning to the herd after escaping the cowboys and believes himself to be safe, he neighs to his herd. When everybody looks up, the twin foals who were grey earlier in the movie are now brown.
When the colonel is about to shoot Spirit, he cocks the hammer on his Remington revolver but when Little Creek runs into him, the hammer is uncocked.
When Spirit is first tied to the polls and retrained for Murphy to groom him, the ropes around his neck disappear, leaving only the ropes around his head like a bridle.
The Lakota camp had a pen for their horses. Lakota would not have had pens, their horses would've run in a herd that was attended to by the teens of the tribe.
When a young Spirit and the other colts are playing in the water, before being approached by the herd of bison, Spirit is shown drinking water by lapping at it with his tongue, as would a dog. Horses do not drink in this fashion, rather they submerge their mouths and suck at the water.
Spirit claims he became leader of the Cimarron herd, "like my father before me." Young stallions leave their father's herd at adolescence and do not take over from them - if they did, they'd end up mating with their mothers and sisters.
The Colonel's shoulder straps display no insignia. They should have displayed the eagle appropriate to the rank of colonel.
At the beginning of the movie, Spirit talks about how the mustangs belong in the Wild West. In fact, they are feral horses, introduced by humans, and should not naturally be there.
When Spirit first enters the fort, there is a group of soldiers riding their horses in unison. Spirit neighs at them, and one brown horse stops moving and neighs back. The next line of horses behind the brown horse are still walking, but don't move forward.
At one point while Spirit is watching Rain and Little Creek from inside the pen, you can see a bottom portion of his mouth pass through a log in the fence and linger there briefly, as if the log wasn't there.
When he arrives at the Lakota camp, Spirit is fed a pile of apples. Likewise, a fully-grown apple tree is featured in several scenes. Apples are an old-world fruit, and would not arrive in the western United States until the arrival of white settlers and farmers, which the film predates.
After Spirit has fought the cougar and the herd runs over to meet him, there are trees in the background. There is then a close up of Spirit and Esperanza (his mother) and a shot of the foal. Yet when the camera zooms out to show the whole group, the trees are gone.