Audio problem: Before the Tortuga bar brawl the musicians are shown playing their instruments. When Elizabeth says, "I just wanted to have the pleasure of doing that myself," it is quiet in the bar, but the violinist is seen happily playing directly behind her and no sound is heard. (01:08:20)
Audio problem: When Will sneaks into Davy Jones' chamber and tries to take the key from him, as Davy Jones' tentacles slip and hit the notes on his organ, they only fall on one or two notes, but we hear a full minor chord (which would require three notes at equal length from each to be played). (01:24:30)
Audio problem: Just as the waterwheel begins to roll away from the mill, watch Will and Norrington on top of it - the sounds of their swords clashing doesn't synch up with their actions. (01:47:30)
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.