There are several scene in which the same animation is reused for the Colonel Haiti and his elephants march during the song. Since they sing different lyrics during this piece of animation, the mouth movements do not match what they are saying. This is most noticeable when they cross the water.
When Baloo is fighting Shere Khan, the landscape is desolate and littered with dead trees. After the fight, when Baloo is lying unconscious with Mowgli and Bagheera looking over him, the landscape is the jungle again, full of live plants and trees.
When Bagheera drops baby Mowgli off with the wolf pack, he leaves the basket at the mouth of the cave den. When he leaves the baby, the basket is closed and when he looks back from his hiding place, the basket is open.
When Shanti is kneeling by the water at the end, singing, as she fiddles with one of her pigtails and flips it back you can see that it is still tied with the purple ribbon. However, the shot right after she fiddles with her other braid shows both ribbons as missing and her hair loose.
When Baloo and Bagheera enter the ruined city to rescue Mowgli, Baloo opens a door which hits Bagheera in the face, giving him a black eye (we see it a couple of shots later when he looks out from behind the door). Moments after that when Bagheera physically tries to retrieve Mowgli, the black eye is gone, only to reappear after all three of them have escaped the city.
When Baloo and Bagheera are trying to rescue Mowgli from the monkeys, Baloo opens a door smashing it against Bagheera. The door has no handle. The next shot is a close-up of Bagheera's head with the door behind it; the door has now a handle.
During "The Bare Necessities", when Baloo sings "I'll tell you something true", he is in the water up to his chest as he throws up his arms, then belly flops out of the water and floats with his front down the river with his arms crossed in front of him. But in the next shot, as he goes over the waterfall, and splashes into the water below, he is sitting right on top of the water holding his toes.
Hathi, a bull Asian elephant, is the leader of the elephant when in reality elephants are a matriarch society. The herd is led by the top cow elephant (Winifred). Once a bull elephant becomes matured, he would either go alone or join a group of other bulls.
Winifred Hathi's mate is apparently the only female elephant in her herd. In real life elephant herds mostly consist of females while males live alone once they reach adulthood though some males also live in 'bachelor' herds.
Hathi claims Sher Kahn is miles away when Bagheera warns him Mowgli is in danger after the boy ran away as the tiger would kill him while alone. In reality elephants like all mammals except humans can smell animal scents from miles away meaning they should be able to detect Sher Khan's scent.