Other mistake: When Captain Jack Sparrow is swimming up to the surface after ripping the dress off Elizabeth, he is swimming with both of his arms because he has Elizabeth draped over his shoulder. There is a considerable distance between Jack and Elizabeth. Also, when both of them are close to the surface, not only are both of Jack's arms out swimming, it can be seen that Elizabeth's double also paddles with one arm to assist in swimming to the surface. (Slow motion makes this easier to spot, but isn't vital.)
Continuity mistake: When Elizabeth first meets Will, he is so exhausted that he passes out. Elizabeth then examines the medallion around Will's neck (when she says "You're a pirate." Note that the chain is still around Will's neck in that shot, but in the next immediate shot, when Elizabeth turns to face Norrington, she hides the medallion behind her back. No where does it show that she removed it from Will's neck, and at the angle that she pulled the medallion towards her, it would not have slid off from around Will's neck.
Other mistake: When Elizabeth stabs Barbossa, he pulls the knife out and there is blood on it. Why is there no blood on the sword later when he pulls it out of his stomach during his duel with Jack?
Continuity mistake: At the end of Jack and Will's duel, Jack says, "Move away," and Will replies "No." In this shot, Will's forehead is bare. Then when he says "No," again, there is some hair over his forehead. After Jack says, "This shot is not meant for you," the hair is gone.
Continuity mistake: Ragetti gets hit in his wooden eye with a fork, which would cause enough damage to be noticeable but no damage is ever visible.
Continuity mistake: When Elizabeth and Jack are on the island drinking rum, the amount of rum in Jack's bottle changes between shots.
Revealing mistake: When the Interceptor's clubhauling and it shows the stern out of the water, it's obviously a model (although there was a real ship, they used a model for riskier scenes).
Factual error: Elizabeth would not have slept undercovers, nor would she have needed a bed warmer in Jamaica in an un-air conditioned room.
Continuity mistake: When Jack says "If you can spring me from this cell," there are suddenly no bars in front of him anymore. In several shots before this, we see him talking to Will without seeing bars in front of him, but he is still at a fair distance so that it makes sense to put the camera in front of him. But in this shot we actually see the camera move with his face, and we see a bar disappearing to the right, so the camera is on Will's side of the bars, and suddenly we see Jack without bars between the two. (The hole would actually be so big he could get through it and escape.)
Factual error: When Norrington is "promoted" to Commodore (already addressed as an error in and of itself), the promotion ceremony held for him in Port Royal would have been meaningless. A commander-in-chief of a foreign station in the British Navy could indeed promote acting officers beneath him, but these commissions would be unofficial until confirmed by the Lords of the Admiralty in London. And as it appears that Norrington is the commander-in-chief at his station, there would be no one to promote him at all - a governor, such as Swann, did not have the authority to do so. The only actual, official ceremonies of promotion in the Royal Navy was for a captain to be given his commission, and to be "read in" aboard his ship, the formal act of taking command. There would be little cause for celebration until a commission was confirmed by the "Sea Lords," in any case.
Continuity mistake: When Jack is knocked out by the bottle he has one hand raised with a gun to shoot Will but when he is seen on the ground both his hands are up by his head. The gun-hand yes, fine, but the other one would be by his side or in a different position at least.
Plot hole: In the shot where two of the pirates find Jack Sparrow in the prison, you see the moon shine out over Port Royal and the pirate's hand around Jack's neck is skeletal. While this is happening we know that Elizabeth is being led onto the Black Pearl by two pirates. If the pirate in the prison turns skeletal, why don't the pirates with Elizabeth turn skeletal? It's clear that they don't as Elizabeth only discovers the curse later on aboard the Black Pearl.
Suggested correction: This can be explained that on the route from Elizabeth's house to the ship there is a lot of fog, smoke from fires and gunpowder explosions, so the moon doesn't get through. The moon only get through once they are underway again and the fog is cleared. The prison is much further and higher than the town and so the moon does get through (only sometimes) there.
You're very much mistaken. In later scene pirates turn skeletal when marching underwater, at the bottom of the ocean. Moon is easily able to get through water and this smoke isn't thick enough to block the moon.
How does water compare to fog? Of course the moonlight comes through the water, its transparent. Fog isn't transparent. You can go technical and question how much the moonlight is reflected away before the effect wears off, but obviously the effect wears off when there is no direct moonlight hitting them, as is the case with fog and smoke.
Continuity mistake: In the scene when Jack is on the Interceptor for the first time a white X is formed with straps on the guards' uniforms. A few minutes later the strap moves up 3 buttons.
Continuity mistake: The right side of Elizabeth's face is twice slapped very hard (first by Boswain and second by Barbossa) but she never has a noticeable bruise, swelling, or other injury to her jaw or cheek.
Revealing mistake: After Will throws the small axe at the pirate and it hits him, he picks it up again and runs away. But the axe has no blood on it. The pirates do leave blood on weapons, as shown when Elizabeth stabs Barbossa later.
Continuity mistake: When the Pearl chases the Interceptor the sea changes frequently from rough, to (relatively) calm sea. That cannot change that rapidly.
Other mistake: When we see Jacoby lying face down with the axe in his back, we can see how far the axe sticks out. It's not deep enough in his back to stick out with that weight of wood and metal. That axe would never stand upright, it would fall to the side.
Audio problem: After Jack saves Elizabeth at the beginning of the movie, Norrington is searching his weapons. As he takes out Jack's compass he opens it and in the next shot you can hear the clicking of the closing compass although the compass is still open.
Factual error: During the attack on Port Royal, at the beginning of the movie, the guns on the Black Pearl are firing at a far greater elevation than they would have been able to at the time.
Other mistake: Translate problem - only in Hungarian version. In the scene, when Jack and Will are fighting, the blacksmith hit Jack from behind. Captain Norrington arrives, and say: Szép munka, Mr. Swan. (Good work, Mr. Swan.) The blacksmith's name is Brown.