When Steve is Singing "Welcome to the Dollhouse", his lip movements do not match up with the words when the scene is up close of him about to finish the song. this is due to another actor dubbing his singing voice.
While in the gymnasium listening to a speech, there are three bullies sitting behind Dawn spitting spit balls at her. She is spit ball-free in one shot, but in the next shot, a close-up, she has several on her.
When Dawn is talking to Brandon in the clubhouse, she is leaning over so her bra (or perhaps a white undershirt) is showing through her sweater. In the exact same shot a few seconds later, it's covered up, even though she hasn't moved.