After the Duke and King climb aboard Huck's raft, they should have been hit by the wake of the passing riverboat.
When the group is counting their take, one mentions "a lead nickel". Nickel five-cent pieces were not issued by the mint until after 1867 - after the Civil War.
All through the movie Jim and Huck talk about going down to Cairo. That would mean they started in Minnesota, Wisconsin, Iowa, northern Missouri, or northern Illinois. Most of those are not slave states. If they had to get to Cairo. A lot safer way to do it, for Jim would have been to simply cross the Mississippi from Missouri (which was a slave state) to Illinois and simply walk to Cairo. He would not have had to worry about that route. It's not covered why they need to get to Cairo so quickly. And therefore had to use the river. Why they just didn't keep to the Illinois side of the river. So they could ground their boat in Illinois if threatened.