Kraken?

[Midhav]

If you look closely in Dead Man's Chest when Jack visits Tia, you can observe that Barbossa is sitting in the other side of the room, unnoticed (Jack the monkey also runs to his side of the room). And if you've played the At World's End game, you'd know that Tia Dalma was using her aides to help her in rallying up the pirate lords, when Jack began his search for the key. It can be assumed that she predicted what was going to happen. Otherwise why would she revive Barbossa so early?

So the only rational outcome of this, adhering to PotCo's existence, would be that this was between the first and second movies. If it was set prior to or during the 1st, then Hector would be the cursed captain of the Pearl. And it's highly improbable for any of these events to occur in the very short time frame of Dead Man's Chest (also, Liz and Will won't be on Port Royal - they'd be roaming about the islands). And there was a long one year difference between the first two movies. And if during the 3rd, then Jack would be dead, and the rest of the characters elsewhere. If after the 3rd, most of these characters would have going their separate ways - Will taking the Dutchman, Jones' crew not being mutated, Elizabeth being a pirate captain, Beckett being dead, Jones dead, the Governor dead, and so many other characters misplaced.

This is the only time period for any of PotCo's events to happen.

And Soccer526 is right - the Black Spot is a sign of the Kraken on your tail.