Thomas Nickerson was not the last survivor of the Essex as stated in the movie. Both Owen Chase and George Pollard were alive in 1850. Owen Chase died in 1869 and George Pollard n 1870. In fact, Chase wrote Narrative of the Most Extraordinary and Distressing Shipwreck of the Whaleship Essex in 1821. This book would have been available to Herman Melville for research.
At the beginning of the voyage when the Captain has too much sail going into a squall, Mr Chase and Mr Joy each cut a line to bring down a sail. In heavy winds the lines to the sails would be extremely taut or possibly jerking wildly. Mr. Joy's line has slack in it and is not jerking. Also, in those winds an experienced sailor would not grab the line with his bare hand - especially on the side of the cut that will still be attached to the sail.
The interview between Melville and Nickerson is set in 1850. After that interview is over and Melville is leaving, the characters discuss the rumors that (petroleum) oil has been discovered in the ground. The discovery of oil in Titusville, PA, by Colonel Edwin Drake, occurred in August 1859, and is considered the beginning of the "oil from the ground" industry, and that was roughly 9 years after the interview took place. Abraham Gesner's first patent for kerosene was granted in 1854, also following the interview in the movie, and it was distilled from oil shale and bituminous coal.
While the film depicts Owen Chase as older and more experienced than Captain George Pollard, Pollard was in fact older, being 29 when Essex sailed to Chase's 23. While Essex was Pollard's first captaincy, he had actually been serving as an officer aboard her for eight years of highly successful and lucrative whaling voyages. The tension between the two men was significantly played up for the film.
Owen Chase did not, as stated, relocate his family after the Essex incident to become a merchant captain. Instead, he relocated to New Bedford, MA, and continued to captain whalers for over twenty years. Captain Chase eventually became wealthy enough to have his own whaling ship, the Charles Carroll, built.
Thomas Nickerson is 14 years old when the story starts. At time of the shipwreck in 1821 he's about 15, 16 years old. The book of Herman Melville is published in 1850, so 29 years after the shipwreck. When Nickerson is telling his story to Melville he should be around 44 years old. In the movie, Nickerson, played by Brendan Gleeson, is not in his forties, but much older, close to his sixties.
While George Pollard did indeed never sail again as Captain of a whaling ship after the Essex and Two Brothers both sank, he made one voyage on a merchant vessel so the insinuation that he never sailed again is inaccurate. It is possible the filmmakers were referencing the end of his whaling career, although this is not stated.
At the end of the movie European House Sparrows can be heard chirping. The invasive species was not introduced into North America until 1851 (16 individuals in New York). They were not established until late 1800's.
Near the end of the film, subtitles reference the title of Melville's novel as "Moby Dick" (with no hyphen). The actual title of the novel is "Moby-Dick; or, The Whale" so even with the customary shortening, the title is "Moby-Dick" (with a hyphen).
At the end of the movie, as the survivors are returning to Nantucket, the caption says the month is June, yet everyone is dressed in heavy clothing, and the breaths of the actors are clearly visible. Nantucket is cool in the summer but not that cool, suggesting the scene was filmed at another time of the year.
The goof item below may give away important plot points.
Towards the end of the film, when 1st Mate Chase is walking up the dock in Nantucket after their ordeal at sea, we see him speaking while standing in front of some crates. Philips head screws are easily recognizable at the corners of the crates and not available in the 1820s.