Continuity mistake: When Travis finds Arliss and Old Yeller in the drinking water, he throws a rock at Old Yeller. Old Yeller is wet all over. Arliss then throws a rock back at Travis, and a chase ensues. After their mother breaks up the fight, she admonishes Travis. Travis then says something to Old Yeller. Old Yeller is lying on the ground dry as he can be. He was just in the water a little over a minute ago, yet there is no sign of wetness at all in his fur. (00:15:45 - 00:17:11)
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.