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Incorrectly regarded as goofs
(at around 1h 5 mins) After Davy Jones wipes the "black spot" from Jack's hand, Jack looks at it and you can see a black mark still visible on the back of his hand between his thumb and finger. The dirt on his hand between his thumb and index finger is there to cover up a tattoo of Johnny Depp's. It is not part of the black spot, which is only on the palm.
(at around 2h) When the Flying Dutchman first gives a broadside to the Black Pearl, it does a fair amount of damage to the Captain's cabin stern windows. Yet when the Pearl is fired upon by the Dutchman using the "triple guns", the damage isn't there anymore.
(at around 42 mins) When Jack Sparrow escapes the cannibals and falls through multiple bridges in the canyon there is a river below but when Jack "lands" he is in the jungle.
Every time it is raining, the characters' faces are dry in close up shots. When the camera pulls back, the body is drenched as it should be in a heavy rain storm.
(at around 37 mins) When Jack is about to be roasted, the native who runs across the bridge with the fire has sticks going through his right ear. Then they do a close-up the sticks are in his left ear. Then in the next shot they are in his right again.
(at around 2h 5 mins) As Jack is rowing away from the Pearl, he turns around to look at the land behind him. As he is doing so, he is holding his compass and it's open. When he turns around to face the Pearl again, he reaches down and pulls out his compass.
At the beginning of the movie there is heavy rain. The soldiers arrive with their rifles slung upward. Soldiers know to sling their rifles downward in the rain so raindrops don't get in the barrel and foul the powder and shot.
When Captain Jack uses the skeletal leg to row the coffin, The end of the leg should have a hip joint but has a knee joint instead.
Monkey Jack was cured from the curse of immortality together with the rest of the crew at the climax of Pirates of the Caribbean: The Curse of the Black Pearl (2003). However, in the post-credits scene of that movie, the monkey takes a coin, therefore making himself immortal again for Pirates of the Caribbean: Dead Man's Chest (2006).
(at around 1h 5 mins) After Davy Jones wipes the "black spot" from Jack's hand, Jack looks at it and you can see a black mark still visible on the back of his hand between his thumb and finger. The dirt on his hand between his thumb and index finger is there to cover up a tattoo of Johnny Depp's. It is not part of the black spot, which is only on the palm.
There's a common misconception that references to Singapore in the series are anachronistic, based on the erroneous notion that the island was named by Sir Stamford Raffles in 1819. It was actually named "Singapura" by a Malay prince in the 14th century.
(at around 1h 50 mins) When Jack first begins to run inside of the giant wheel, he bumps his head on a crossbeam. When they are all running inside the wheel later, you can see that the crossbeams are "higher" to the middle of the wheel. He shouldn't have been able to bump his head.
When Will and Jack are looking out on the Flying Dutchman (Will holding a lantern) two people walking behind them are cut in half by the green screen background. In other words, their heads float by on air.
(at around 1h 55 mins) When the large water wheel with Norrington and Will Turner rolls into the water where Jack and Elizabeth are fighting Davy Jones' crew, it does not leave a wake when it rolls past Elizabeth and falls over on its side. It must be CGI, as an actual body moving through water would have left a wake.
(at around 39 mins) When Will and the crew of the Black Pearl begin rolling the cage in which the cannibals had placed them there is a clear face-shot of Gibbs' stunt double.
When Elizabeth pulls out the compass to check the heading, Keira obviously pulls the string to control the movement of the arrow, making it point to Jack.
At 1h 54m 1s the (slain) guy who previously fell backwards into the sea starts to get back up again.
When the water wheel falls over on the beach, Will and Norrington fall out and have trouble with balance. They both exit the wheel at the same time, yet Norrington runs towards the dingy almost immediately while Will still has trouble walking a straight line.
During near the end of the movie, when the crew encountered Davy Jones, Jack sings "I've got a jar of dirt! I've got a jar of dirt! And guess what's inside it?" was not on script. You can see the confusion in Will's eyes and he looked at the director to see if it's scripted or not.
At 2h 11m 40s a black fly crawls all around the top and front of his wig as he leans into camera. This continues for one and a half seconds or more.
(at around 1h 18 mins) When Jack Sparrow, Elizabeth and Norrington are arguing on the pier in Tortuga, the hull of a ship can be clearly seen behind them bearing a Plimsoll line, which wasn't used until the late 19th century.
(at around 1h 50 mins) When Jack Sparrow falls into the grave, the print of a modern shoe can be seen clearly in the dirt at the top of the grave.
The movie is set between 1714 and 1727 (dated by the signature George R. in the letters of marquee). However, there is a painting hanging on Beckett's office depicting the Battle of Cape St. Vincent, which happened in 1797.
At around 1 hour and 44 minutes, Davy Jones says "Down then!", but his mouth continues moving for several seconds afterwards, even though he isn't saying anything.
In the start of the movie, Jack want's to find the key to the chest of Davy Jones so that he can force Jones to call the kraken off from it's hunt for him. However, the key is not needed for this. Jack could simply find the chest and threaten to blow it up with a cannon. (like Beckett does in At World's End.) Later in the movie he also goes to find and dig up the chest without having the key.
In the beginning, why is Elizabeth sitting outside in the rain? No reason is given, since Will and she had not been taken by surprise by the soldiers for arrest yet. It seems unlikely for a rained-out bride to sit outside in the rain, ruining her hair and dress, especially before the discovery of modern medicines like penicillin. Catching "your death" of cold was a very real concern.
(at around 33 mins) Gibbs hints to Will that the crew's bone cages were made from the bones of the Pearl's missing crew members. However, those same bones are far too large to be human. The bones are also too aged to have been made from the rest of the crew.
(at around 48 mins) When Master Gibbs is telling the tale of the Kraken, Masters Pintel and Ragetti appear to have no knowledge of the Kraken, but later in the movie (at around 1h 40 mins), when they are rowing the boat ashore, they have a heated discussion as to the proper pronunciation of the Kraken, as if they had known it all along.