Factual error: In the opening narrative about the first person to call out "America", as the ship passes the Statue of Liberty, it's traveling in the wrong direction - with the Statue entering the screen from the viewer's left and moving toward the right; a direction that would have taken the ship from Manhattan to Staten Island (or through the Straits into the Atlantic).
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.
Character mistake: While listening to the fixed record at the antique music instrument shop, Chris talks about 1800 instead of 1900. (00:30:45)