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.
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.
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 Essex was three masted (probably bark rigged) as described in Chase's own book about the voyage. The vessel in the movie is two masted (a brig)
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.