When Mowgli, Harrison and Chuchundra are running on the trains roof, they are running towards the train's end. People in the windows are looking in the opposite direction.
When it's morning in the cave, Mowgli is sitting with two wolves. In the next shot there's only one wolf.
The scars on Mowgli's side are missing in some shots.
Harrison's rifle a Lee Enfield bolt action is clearly seen fitted with standard iron sights, yet when he looks through them you see a cross-hair as if he had a telescopic sight (not invented yet at the time this was set anyway, the lee Enfield itself would have been brand new)
Harrison's rifle, a bolt action Magazine Lee-Enfield, was first manufactured in 1895, whereas the film is set in 1890 (at 0:02:35). The Magazine Lee-Enfield was a re-manufacture of the Magazine Lee-Metford bolt action rifle first manufactured in 1888, but that is not the rifle Harrison has.
Chimps do not live in Asia, where the movie takes place.
Baloo is played by an American Black Bear (Ursus americanus). As the action takes place in India, it should be an Asian Black Bear (Ursus thibetanus) or a Sloth Bear (Melursus ursinus).