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: After reuniting with Simba, one of Nala's paws changes its place on the ground between shots. When Simba denies being the king, he begins to walk off screen to the left. Here, Nala stands several feet away from Timon. But by the next shot one of her paws is suddenly inches behind Timon instead.