Factual error: The Portuguese slave ship Tecora was one of the most notorious of the illegal slave ships, but no slaves were thrown overboard in mid-ocean as shown in the film - at least on the trip in question. The Portuguese were pros at the slave trade and had plenty of food on board to feed their "cargo" between Sierra Leone and Cuba. The only time a slave would be thrown overboard in mid-ocean was if his/her health posed a serious risk to the crew and "cargo". (Slaves were too valuable to just throw away for the price of their food.) Historically, though, there were instances where whole cargoes of slaves were tossed overboard. The British Royal Navy zealously patrolled the waters off West Africa to try to shut down the slave trade. If a British ship was sighted, the slavers sometimes tossed slaves overboard to destroy the evidence and prevent the seizure of the ship.
Factual error: Cinque is shown in the first scene of the film ripping a nail (to pick his shackles) from the lower deck of Amistad with his bare and bloody fingers during a storm. In fact, Cinque was topside one day, and simply stooped down to pick up a piece of metal he saw to use as a pick. (Not quite as dramatic, but true.)