Continuity mistake: When Norrington and Elizabeth are talking about how Will ended up on the Dutchman in the shots of Norrington you can see it's raining though not heavy. In the shots of Elizabeth however it's not raining despite being stood in front of each other. (01:29:00)
Continuity mistake: During the three way fight for the key, Will uses the bell rope to grab the key from Norrington. A couple of minutes later, while they are fighting on the roof, Jack sneaks up behind them and tries to snatch it from Norrington, despite already having taken it. (01:49:00 - 01:51:00)
Suggested correction: Norrington takes it back from Will during their fight on the roof (not seen but possible), only then Jack tries to take it again.
Other mistake: When Elizabeth points to the word "Tortuga" written in flames, she is pointing the wrong way. (01:04:30)
Other mistake: When the two pirates are rowing toward the beach, and the dog is at the front, one of them is reading the bible. From the cover it's being held the right way up, but in a very quick shot showing the actual text of the book, the text itself is upside down. (00:30:20)
Suggested correction: This isn't a mistake. Pintel states that Ragetti can't read. So the fact that Ragetti has the book upside down adds to this claim. With regard to the cover and text being opposite ways round, Ragetti or someone could have reattached the cover at some point as the Bible is damaged in places.
I feel like arguing that the "cover may have been reattached" is far too much conjecture to be a mistake. It's much more likely to just be a minor continuity gaff as the mistake suggests.