Continuity mistake: In the scene when Will is talking to Cutler Beckett, there is a clock behind them that is being hauled up at a very slow pace. But when the shot switches and there's a close-up on Will, the clock has disappeared. Despite the angle change, we should still be able to see the clock. There hasn't been enough time for it to have moved out of shot. (00:11:20)
Suggested correction: Actually the clock is simply out of shot. If you listen you can hear the creaking where it's still moving and if you watch the two ropes behind Will you will see they are still raising and on the post behind Beckett you can see the shadows raising too. So the clock just simply isn't in the shot.
Continuity mistake: When Pintel and Ragetti's boat flips, the boat is seen firmly secure on the beach, well before they end up on the beach. That would only be possible if the waves crashed on the beach with a great force. (00:30:30)
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.