Revealing mistake: When the boat is supposedly surrounded by a swarm of flies, they're really just relatively few flies trapped between two panes of glass in front of the camera lens. Evidence: whenever the camera moves, the "swarm" moves with it against the background, and you can even see some of the insects walking on the surface of the glass.
Continuity mistake: When Charlie Allnut grabs a bottle of gin from the box, all the bottles in it are wrapped with paper for transport. But when Rose Sayer takes the bottles out of the box to empty them into the river, the paper is gone (from the movements of her hand/wrist, you can tell that she doesn't unwrap the paper from the bottles).
Charlie: All this fool talk about The Louisa. Goin' down the river.
Rose: What do you mean?
Charlie: I mean we ain't goin' to do nothin' of the sort.
Rose: Why, of course we're going! What an absurd idea.
Charlie: What an absurd idea! What an absurd idea! Lady, I may be a born fool, but you got ten absurd ideas to my one, an' don't you forget it.