Visible crew/equipment: After Will is captured, when Jack first opens his make-up laden eyes, the white square reflections of the reflector shield is visible in his eyes; as it is in other characters' close-ups as well. (00:25:05)
Visible crew/equipment: At Tia Dalma's, two large white rectangles - either a light fixture or the reflector screen - are reflected in the glass bottle, which hangs beside Jack's head. (00:49:50)
Visible crew/equipment: While Norrington and Will begin their duel, Jack walks away and promptly falls into the open grave. In the shot of Jack from within the grave, the imprint of a modern, flat bottom trainer/sneaker sole can be seen on the dirt wall (yes, wall) to Jack's left. It is not the imprint of a shoe of the time period. (01:48:00)
Visible crew/equipment: When Jack opens the compass on the deck, two round lights are reflected on the lid. They are obviously stage lights, since from another point of view neither the sun nor any type of light is seen.
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.