Deliberate mistake: At the beginning of the movie Mr. Coates tells his wife that he will be gone "all of three months, maybe four." The first time we see Bud and Elizabeth Searcy she tells Travis that her dog is pregnant and that Old Yeller is the father. We then see her dog that does not look very pregnant. The next time we see Elizabeth she presents Travis with one of the pups. The problem is that the pup that was supposedly just born is about 4 months old.
Factual error: In one scene where Travis walks out the door of the kitchen half of the cabin, there is a thermometer nailed beside the door. In the late 1860's, when the movie takes place, thermometers like that were not available.
Other mistake: When Travis shoots Yeller, his gun (a .50 Cal black powder rifle) doesn't kick at all. Ordinarily a gun of this type kicks hard enough to leave a bruise.