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 - following the Civil War.
All through the movie, Jim and Huck talk about going down to Cairo, Illinois. That would mean they traveled through Minnesota, Wisconsin, Iowa, northern Missouri, or northern Illinois. Most of those were not slave states. If they had to get to Cairo, a much 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.