Deliberate mistake: At the elephant graveyard, little Simba claws Shenzi in the face. When Mufasa saves Simba from the hyenas, the cuts are gone, a few seconds later. [This was done intentionally, I'm sure, for two reasons. The first being, Disney doesn't let fresh scars linger on the screen too long. Secondly, during that same scene when Mufasa rescues Simba & Nala, he claws Banzai in the rear. To stress the point later in the movie, that severe scar is shown too, but only briefly, it too disappears because of reason 1. Still a "mistake", but there's why.]
Continuity mistake: The whites of Simba's eyes change frequently through the movie, from yellow to white. They're yellow up until the scene where Pumbaa, Timon, and Simba are stargazing; after that they change back and forth frequently. During the Mufasa-in-the-sky scene, when Simba asks, "How can I go back? I'm not who I used to be," they change from yellow to white and back within three frames.
Trivia: Disney wanted people to despise Scar, the film's villain, so, during Scar's big song 'Be prepared', they made references to Adolf Hitler. When Scar's army begins to march, they are goose-stepping like Nazi soldiers and have their snouts raised like a Nazi salute (their snouts appear longer here than in any other part of the movie, and pointed to their right). Scar is on a large ledge, which resembles a balcony, much like that used by Hitler - on the side, the rock has a pattern resembling a giant Swastika. And finally, on the ground where the army marches, lines appear. These lines were on the streets of Germany, where the Nazis paraded.
Pumbaa: Hey, Timon, ever wonder what those sparkly dots are up there?
Timon: Pumbaa, I don't wonder; I know.
Pumbaa: Oh. What are they?
Timon: They're fireflies. Fireflies that, uh... Got stuck up on that big bluish-black thing.
Pumbaa: Oh, gee. I always thought they were balls of gas burning billions of miles away.
Timon: Pumbaa, with you, everything's gas.