Factual error: In the opening scenes of the film, the audience finds that Tom Hollander has warrants for the arrests of Orlando Bloom and Keira Knightley for a number of charges, one of which in conspiracy. However, while conspiracy is considered a distinct charge under American law and jurisprudence, this is not nor was it the case under British law. According to the principles of British common law and jurisprudence, conspiracy to commit a crime is legally identical to the commission of said crime (e.g., conspiracy to commit treason is considered treason). (00:03:20)
Factual error: At the bar in Tortuga, one of the three musicians is seen playing the 'concertina', but it was not invented yet. Sir Charles Wheatstone, an English physicist (b.1802 - d.1875), invented the 'concertina' around the mid 1800's. The 'concertina' is a small musical instrument like an accordion, with bellows and keys. (01:06:10)
Factual error: The helmsmen on the ships always spin the wheel in the direction that they wish to turn. However, in the days of sail the wheel had to be spun in the opposite direction from the direction of turn. (01:56:00)
Factual error: When Jack shoots at the hanging barrels of gunpower and rum, in the final battle with the Kraken, he fires a ball (presumably lead) as seen in the slow motion. However this would not cause an explosion as shown. There wouldn't be a spark for ignition. (02:05:00)
Factual error: The formal title of the East India Trading Company is the Honourable East India Company or HEIC; official merchandise provided by said company would not be affixed merely with the letters EIC but rather HEIC.
Answer: The jar was to put Davy Jones heart in. He can't touch dirt ever again since he failed to keep up his duties which means he wouldn't be able to get his heart back.