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.)
Continuity mistake: When the Amistad is captured by the American naval vessel, and Cinque jumps out of the dinghy to swim for it, the frontal shot of his face with the pursuing boat behind him shows the sun overhead, at midday or morning, towards viewers' left. When the shot changes to behind him (chaser's view), the sun is dead in front of him and setting.
Factual error: No presidential candidate campaigned in person until William Jennings Bryan was nominated the Democratic candidate in 1896. Before Bryan, it was the practice that candidates campaign only in their hometown (candidates are to "stand" for office, not "run" for office) while their supporters campaign for them nation-wide.
Audio problem: When Baldwin writes to John Quincy Adams begging for help, Adams crumples up the letter and drops it to the floor. As it comes to rest, you can see the word "threatened" written above the words "need you". But in the voice-over reading the letter out loud, the word "threatened" is never spoken.
Factual error: At the end of the first trial when the judge said that the Africans are free, he also ordered the immediate arrest of Luis and Montez. According to historical records, they were not even in the country, much less present at the court proceedings. In fact, the Africans had already had them arrested on charges of assault and kidnap. They both paid bail and went back to Cuba.