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.] (00:21:50)
Deliberate mistake: In the scene where the bad guy is attached to the missile and fired, in the split second before it hits the helicopter you can see below it a building called SUN BANK, but the letters are backwards. A close look reveals the likely reason - to the right of the reversed building is one which looks just like the building to the LEFT of the Sun Bank building behind the harrier a few seconds earlier. Most likely they couldn't film the chopper from the right side because there was a building there (the one the camera flies through), so they filmed it from the other side (the same side they'd filmed the harrier from), catching the "Sun Bank" behind, then had to flip it to have everything facing the right way. (02:06:55)
Deliberate mistake: In the scene where Forrest is describing his heritage, the clip of KKK on horses is taken from The Birth of a Nation. In this clip, you can see tire tracks on the dirt road well before automobiles were supposed to be in existence. Robert Zemeckis decided to leave this mistake in to perfectly match the clip to the original movie.
Deliberate mistake: When the crow drops Shelley's ring into Sarah's hand at the end of the film, the sound of metal upon metal is heard. (01:30:00)
Deliberate mistake: When young Odette is sliding down the banister, and gets stuck spinning around the end of it, it would be impossible to spin like that without her legs hitting the rail that she just slid down.