Continuity mistake: When Jack speaks with Elizabeth on the dock and asks, "Are you certain? Is that what you want most?" the kohl very noticeably does not go around his entire left eye in this close-up, but, in previous and following shots it does. (01:15:10)
Continuity mistake: When Jack and Gibbs walk on the dock towards the Pearl, they pass a couple kissing, as Elizabeth calls out to Jack. In the following shot, that couple is much farther (about 10 ft) up the dock, away from the Pearl - note the other ship's exterior, behind them. (01:17:00)
Continuity mistake: After Jack explains the legend of Davy Jones to Elizabeth, and they have found their heading, Elizabeth's braid is going down her back. When Jack points Elizabeth toward the ship her braid is now on her right shoulder. She doesn't move her head and there is not enough time for her to move it herself. (01:17:00)
Continuity mistake: When Cutler Beckett plays with Norrington's sword, as he begins to speak with Governor Swann, the step ladder is to Beckett's right - note its shadow on the wall map. The ladder and its shadows change positions in the following shots. (01:20:35 - 01:21:40)
Continuity mistake: During the dice game aboard the Flying Dutchman, when Will challenges Davy Jones, the cloth with the key drawing is folded and positioned differently between shots. (01:21:00)
Continuity mistake: After Will challenges Jones he is given five dice - one being considerably smaller than the other four. However, when Will looks under his cup during the game, all five dice are of similar size. (01:22:00)
Continuity mistake: Aboard the Flying Dutchman, when Will sneaks in to steal the key, as the shot draws closer to Jones the quills are shown on the organ keys - with one leaning over the keys. In the next shot, as Will reaches sleeping Jones, both quills are leaning away from the keys, and an extra quill stick (feather free) suddenly appears. (01:24:00)
Continuity mistake: When Elizabeth, Jack and Gibbs speak on deck about Beckett wanting the chest, the flask's black strap repeatedly jumps over and under the cloth round Gibb's neck. (01:27:30)
Continuity mistake: On the Pearl, after Elizabeth tells Norrington that she trusts Jack, when Norrington walks away from the deck rail, in the shots facing Elizabeth, the pretty cumulus clouds behind her change back and forth between shots. (01:28:50)
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: When Will has been rescued from the Flying Dutchman and they go up on deck just before the kraken attacks, Will is on deck. A moment later he is seen on top of the mast, with no time to have got up there. The others who had come up from the cabin had only just emerged. (01:30:50)
Continuity mistake: After Captain Bellamy tells Will it's strange to come upon a long boat in open waters, he asks, "And what are we running from?" as he stands with his hands behind his back, between two sailors. Yet, in the next shot from behind, Bellamy stands at the end with his arm down, but next shot he's back to the original position. (01:33:00)
Continuity mistake: After the ship with the "bride spirit" is attacked by the Kraken, Will ends up underwater, and when he surfaces his hair is soaked and slicked back, as he climbs on the ship's debris. However, in the next shot, his hair is parted, stringy and falling to the front. (01:33:50)
Continuity mistake: When Jack "intuitively" inquires about Elizabeth's feelings, the dangling beads in his hair are over his dreadlocks, near his shoulder. Next close-up they're tucked under his hair. This type of thing - with all the do-dads in Jack's hair - occurs numerous times throughout the film. (01:35:20)
Continuity mistake: After Will slides down the sail, just as he grabs hold of the mast line, the cut sail is only tied down at its corners. After he puts the knife in his mouth, the sail is also tied down directly under the cut. (01:36:10)
Continuity mistake: When Elizabeth questions Jack about his "broken" compass as they stand on deck, her left arm rests on the deck rail and changes position back and forth between shots. (01:36:30)
Continuity mistake: When Pintel and Ragetti argue over the pronunciation of "Kraken" while they're rowing, the loose end of Jack's red bandanna changes position and jumps from his back to over his shoulder, between shots more than once. (01:38:30)
Continuity mistake: On the island, when Jack says, "Yes, it does. You're sitting on it," the compass lid faces away from Elizabeth, but in the next shot as Jack shoos her away, the compass faces her; and the rope changes position too. (01:39:30)
Continuity mistake: In the scene where Ragetti is balancing the shovel in his hand, he is balancing it in his right hand. Then when we see him through the scope, however, he is balancing it with his left hand (he is still facing us). Then when we cut back to him, he is holding it in his right hand again. (01:40:00)
Continuity mistake: When they dig up the chest and Will arrives, there are long shadows. Yet, when Jack, Will and Norrington duel, they have very short shadows directly beneath them. The large chest's shadow changes as well. (01:40:20)
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.