Continuity mistake: At Tia Dalma's, when Will tosses the knife at the tabletop, there is a tall slim candle beside his right hand. However, in the next shot when Tia Dalma says, "Against the cold and the sorrow," the candle beside his right hand is now very short, though no time has passed. (This doesn't refer to the short, wide candle in both shots.)
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.
Suggested correction: Not true, the official historic merchant's mark of the company literally shows EIC as an abbreviation.
Revealing mistake: When Jack, Elizabeth, Norrington and the crew are sailing to meet the Dutchmen, you can see the water is moving past the Pearl, showing the Pearl in motion on the water. There is then one shot of Elizabeth and the sea behind her is completely still and not moving past the Pearl. Camera cuts and again the sea is moving past the Pearl.
Continuity mistake: When Norrington, Elizabeth and Jack find the chest they wipe some sand off and there are black parts of the chest visible. When they pull the chest out of the ground, all the black bits are gone and is covered in sand.
