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: Secretary of State John Hay is depicted issuing the order to "initiate hostilities" against Spain. Unfortunately, at the time we actually went to war with Spain, John Hay was not the Secretary of State. That position was held by William. R. Day. Hay did not become SofS until September of 1898, after most hostilities had ended.