Audio problem: When Nighthob and Teeny are talking to the Rockbiter near the beginning of the film, Teeny says to Nighthob "This could be serious", then turns to Rockbiter and calls out his name. Watch Teeny's mouth as he calls out "Rockbiter". You will see a very blatant editing mistake as Teeny is not actually saying 'Rockbiter", but is saying the next line that follows.
Continuity mistake: Atreyu climbs up a tree and talks to the Ancient One. There is a series of face-on shots of the boy alternating with ones from behind him. In the face shots, Atreyu's left hand is below shoulder height on a branch. In the shots from behind, his left hand is holding the branch well above head height.
Continuity mistake: When Atreyu first sets out on his quest, his horse Artax is grey with dark mane and tail. However, when they stop to rest and eat by the stream, Artax is white with white mane and tail. By the end of the film, when Bastian and Falkor flies over Fantasia,they spot Atreyu and Artax - low and behold - Artax's mane and tail are dark again.