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.
Deliberate mistake: The mechanic points out the overhead installation of the indicator compass. He says "Want to see where I put the compass? It's the best place I could find for it." The installation site was planned, not improvised. In order to read the compass in a mirror the compass was specially ordered from the manufacturer with the numbers reversed so it could only be read in a mirror. This mistake was intentional in order to claim a mirror was needed from a bit character.