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.]
Other mistake: (May only apply to the original VHS release.) When Scar has Zazu locked up in a cage, Zazu mentions Mufasa's name and Scar yells at him, "What did you say?" Right before Scar's actual line, whilst Zazu is talking, you hear Scar's "What did you say?" line very faintly in the background, even though Zazu has not even mentioned Mufasa yet.
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.
Question: We're only told about two males in the pride, Mufasa and Scar. Who was Nala's father? It can't be Mufasa because then she and Simba would either be siblings or half-siblings and they wouldn't have got together. And it can't be Scar because she called him by his name, not Dad, and she and Simba would still have been cousins.