The real tearjerker "Can't Take Me" as Spirit is captured by the wranglers and dragged to the fort, fighting them every step of the way.
Inferred Holocaust: Spirit returns to his herd, but history says guys like the Colonel eventually won. Today, the prairies are mostly farmland, and wild horses are rounded up by the herdful to make room for this. Not to mention that there was a railroad line scheduled to run across Spirit's homeland, and they certainly wouldn't abandon a project of this scale just because of two exploded locomotives, which means that sooner or later his herd would have to deal with trains passing by all the time. Indeed, Spirit: Riding Free shows his son having to live with human settlements as a result of the train.
Misaimed Marketing: A figurine of Spirit, Rain, and their foal came with a description of the Bureau of Land Management's annual mustang roundups and the importance of "adopting" a wild mustang. Not only does this run counterproductive to the film's message, but the BLM's roundups routinely result in dead horses.
Stallions are not the leaders of a herd; mares are. Stallions guard the back. This might be more a case of Acceptable Breaks from Reality though as seeing Spirit simply run at the back of the herd wouldn't have been so awesome.
That Spirit survives the movie at all is a small miracle. Mustangs are hardy, but not that hardy.
The horse handling. When Spirit first comes to the Army fort, and they attempt to break him. the way they tied him down to brand him was inaccurate and hazardous. Even in the old West people were wise enough to not mount a completely wild horse with full tack, in a large rectangular arena. The way Spirit juggled them, most of the riders should have broken bones, if not necks and skulls. Not to mention the first thing an actual regiment would have done to a mount prospect: Geld him. It's always a possibility that he was considered such a fine stallion that they wanted to keep him for breeding as well as riding, or even that they planned to do the gelding later.
The Native American version of breaking him to ride was a lot more like methods of Western-style breaking in use today, although nothing like the way Plains Native Americans trained horses, so the creators clearly had some idea what was correct and probably did it the other way make the soldiers look like jerks and morons. (If that was what they were after, it worked.)
A mild example, but still noticeable: when Spirit frees the other train horses he does this by kicking one chain off with three kicks of his hind legs and the other with two kicks of his forelegs. Realistically his hind leg kicks should have broken the chain off faster as horses have twice the power in their hind legs as they do in their forelegs.
Horses are not indigenous to the Americas. Then again, it's not like Spirit is likely to know that: as far as he knows, his kind have been wild for countless generations.
Uncanny Valley: The weirdly intelligent horses with eyebrows drop some viewers into it.
Visual Effects of Awesome: Horses are traditionally considered one of the hardest animals to animate, and the animators got them down beautifully.
The Woobie: The wrangler's horse that first urges Spirit to run. He only appears briefly, but his guilt and anguish when Spirit is captured are extremely palpable. It's clear there's a very sad story there.