Continuity mistake: When they are having the "piano duel", Jellyroll Morton stands up in front of the piano, and his chair slides back about a metre, the scene cuts to the audience, and then when it comes back a second later, the chair is back right behind him again.
Continuity mistake: Near the middle of the movie when 1900 and his best friend meet for the first time, the ship is tossing and turning and his friend vomits into a bowl or a shallow vase, then the camera angle switches and you can see inside the bowl and it's empty.
Continuity mistake: After the girl gets off the ship, 1900 breaks up the record that he recorded earlier on. The thing is, it's supposed to be the same one that his friend plays at the end, but the pieces that are fixed together don't match the way he broke it.