In full dress, Captain Fitzgerald wears the epaulets of a Royal Navy commander, not captain, and the belt of a lieutenant. In undress, he wears the single-breasted "morning coat", which was abolished by the Royal Navy in 1833. He also refers to an "ensign" aboard his vessel, a rank that existed in the British Army but never the Royal Navy where the most junior officer was a midshipman and an ensign was (and remains) a flag (ensign is the most junior officer rank in the US Navy).
Martin Van Buren was never photographed while in office, and in 1839 photography was extremely new technology and not widespread. The first president to be photographed while in office was James K. Polk on Feb 14, 1849 (although William Henry Harrison may have been photographed in 1841 during his very brief presidency.) Van Buren was photographed in 1845, well after he had left office, but he was not wearing a sash as depicted in the movie. Incidentally, John Quincy Adams and Andrew Johnson were also photographed that same year.
As the letter to Adams asking for his help before the Supreme Court is read, the letter states that 7 of the 9 Justices were Southern slave owners. Only 5 of the 9 Justices on the Court at the time were from the South. Justices Story, McLean, Thompson, and Baldwin were natives of the North.
During the first scene with John Quincy Adams, he is being derided by another Congressman. Adams replies by referring to the man as "Representative Pinckney." Although the Pinckneys were a prominent American family in the nation's early years, none of them served in the House at the time of the Amistad case.
During the scene in which Secretary Forsythe talks with President Van Buren about the dire political consequences of the Amistad Africans being acquitted and suggests dismissing the jury and replacing the judge, there is a bowl of water on the desk at which Van Buren is sitting. During the conversation, the water in the bowl inexplicably changes from clear to dark (presumably its purpose is to clear out the unused ink from quill-pens when Van Buren is done using them, to prevent the hollow part of the quill from getting mucked up with dried ink), then back to clear.
In the scene where Adams and Baldwin are studying books before the Supreme Court hearing, Adams is interrupted by Cinque's translator. While the translator speaks, Adams is holding a magnifying glass over the book, but when the camera angle changes he is suddenly holding a pen and writing with it.
As the Africans row to the island for fresh water, their rowboat is marked "LA AMISTAD" in all capital letters. However, as they're returning, after the Navy ship appears, the rowboat reads "La Amistad" in mixed case.
In the Supreme Court scene, when John Q. Adams is making his speech before the justices, he reaches for a document that is handed to him by Baldwin. Baldwin hands him a single sheet with a ribbon seal, but in Adams's hands it becomes the "Review" pamphlet with several pages.
An African becomes misty over the sight of an African violet in the greenhouse of John Q. Adams. African violets were detailed by a German botanist Baron Walter von Saint Paul-Illaire in 1891. They were not imported to the United States until a few years later. Also, the slaves apparently were from West Africa. African violets are only found along the border region of Tanzania and Kenya in East Africa.
In one scene, where Isabella II is dining, a portrait of Louis XIV is hanging in the dining room. Even though Isabella was his Great-Great-Great-Great-Granddaughter, it's very unlikely that the Royal Palace of a Spanish Monarch would have a portrait of a French king prominently displayed, especially one who had been dead for 115 years when Isabella II was born. The portrait is actually hanging in the dining room of "Marble House" in Newport, Rhode Island, where much of the movie was filmed.
President Martin Van Buren did not replace district court Judge Judson with Judge Coglin. He did, however, write a letter to Judson asking him to send the slaves back to Cuba; Van Buren had a boat waiting to take the slaves away immediately, and thus render moot any appeal the abolitionists might make. However, this was still perceived as interference with the court system, and it did play a part -- although perhaps a minor one -- in Van Buren's failure to win re-election in 1840.
Ruiz and Montes were not ordered arrested by Judge Coglin as part of his verdict; the abolitionist lawyers had charged them with assaulting their clients. They were found guilty and sentenced to prison while the main case was pending.
When the Africans are loading up on fresh water, an American ship cruises by with a long stream of water pouring from the side, presumably discharge from a pump or engine. The discharge is near the water line, it's not raining, and the sea is calm. Even under those conditions, the water on deck would flow over the side, not form a long stream.
There is a scene where the men are shown lying on their bunks and their heads are all moving to the rocking motion of the ship. However, there is a chain hanging nearby that is not moving at all. This is because the ship was in port when this scene was filmed and someone out of view was leading all the actors to move their heads to give the impression that the ship was sailing on the high seas.