In the beginning of the tea drinking scene with William, Lord Beckett adds a sugar cube into his tea. The first sugar cubes were invented in the Czech town of Dacice during 1840s, decades after when the movie is set.
When Beckett sets the Dutchman to give no quarter in the maelstrom battle, he orders his officer to make semaphore signals to the other ship. This is done by an officer holding two flags in different positions, the modern way. However, the British Navy in the 18th century did this by hoisting sets of special flags on the masts of the ships, not by setting an officer on deck.
Directly after the battle between the Black Pearl and the Flying Dutchman near the end of the film, Barbarossa says "Belay that, or we'll be a sitting duck!" in response to Jack's command. but the phrase "sitting duck" was not introduced until the early 1900s.
When Captain Jack Sparrow is on the Black Pearl in Davy Jones' Locker, his right hand has several large scratches. But a few minutes later when Barbossa leads the crew to Jack's rescue, those scratches are gone.
When Elizabeth is giving the rousing speech to the pirates on the gunwales of the ship, all the close up frontal shots of her show her hair partly tied up. Rear shots show her hair completely loose but damp and limp. As she jumps down from the gunwales, her hair is loose, dry and bouncy. Will Turner's hair in the same scenes sometimes appear neatly tied back, at other times flying in the wind in his face.
When the three representatives of each side of the war step on a lanky piece of land in the middle of the sea to negotiate, there is a black piece of cloth tied to Jack Sparrow's right hand palm which disappears once during their negotiations and then appears again and remains there until the end of the scene. More precisely, when he is saying the line: "That debt was paid mate, with some help from ... (moving his hand toward Elizabeth)" the cloth is gone and right after it when saying the next line after Davy Jones' :"technically..." the cloth is back and remains till the end of the scene.
Right after the battle aboard the Dutchman, we see Jack and Elizabeth leaving with a made-up "parasail" and they land straight to the sea. In the next scene, we see them boarding the Pearl, and they should be soaking wet since they are just coming out of water, yet no water is visibly dripping off of them. Elizabeth is a little wet from the rain but Jack is remarkably dry.
When Barbosa and Jack come to the island after returning to the real world, as they stand beside the Kraken talking, when the camera is pointed towards the water you see rocks, the angle changes and when it returns, you can see the tentacles floating in the water behind them.
When Tia Dalma has a hold of Barbossa's wrist after entering Shipwreck Cove and telling him it was by her power he returned from the dead, she is making contact with his hand above the cuff. In the next shot, her hand is holding onto the cuff of his coat and not touching the hand at all.
When Jack is laying on the floor after giving up trying to pull his ship, the Black Pearl's shadow is on the right side of the Pearl where Jack is standing. When the scene progresses to the next scene, the shadow is on the left side of the Pearl.
When Will Turner is brought before Lord Beckett, a close-up shot shows Beckett has a decanter in his hand and pours himself a glass as he talks to Will. The next shot is over the shoulder of Will and shows Beckett picking up the decanter, removing its stopper, and beginning to pour the same glass.
When Jack Sparrow is in Davy Jone's locker, he makes a comment about there being no wind at all, but in the shots right after that, some of his hair can be seen blowing in the wind, showing that there actually is wind.
In the scene where Will gives his heart to Elizabeth for safekeeping, after he moves towards the shore, Elizabeth runs to kiss him. While kissing there are no visible trails in the sand on her path (slightly different than Will's), although the waves clearly didn't reach enough to erase them. (Wills' trails are visible though). Later, after the Duchman disappears, her trails are visible instead of Will's and there are clearly less trails behind the rock with the locker than in the first scene.
Singapore Harbour as depicted in the film is apparently surrounded by mountains. In reality, Singapore is a small, flat island whose highest point is Bukit Timah, standing at a mere 164 meters above sea level.
The shot that shows Singapore harbor shows a craggy, rocky harbor. Singapore is in fact an island without any mountains or cliffs and it's highest point is 538ft above sea-level known as Bukit Timah, a hill in the middle of the island.
During the waterfall scene before the ship goes over the side everyone is scrambling about deck. You hear at least two characters including Elizabeth give the command "Hard a port". When this film was taking place the type of commands for steering ships at sea were called tiller commands. The tiller on a ship is what actually moves the rudder and a hard to port command would have made the ship turn right and not left as it did. Tiller commands were replaced by rudder commands in the early 20th century. The modern rudder command would have made the ship turn as it did.
Some viewers have reported seeing braces on the teeth of the young boy singing in the opening scene. In fact, the boy has metal caps on some of his teeth, much like Jack. The only difference is, his are blackened and clearly not made of gold.
It's often believed that the founding and naming of Singapore postdate the period in which the films are set. In fact, the name "Singapura" - "city of the lions" - was first given in the fourteenth century.
Aboard the Black Pearl in Davy Jones' Locker, while the crew is attempting to capsize the Pearl, the charts are on a table on deck. Nowhere is it seen that Barbossa, who was standing next to them, or anyone else grabs the charts. So, when the ship capsizes, the charts would sink in the ocean along with other loose object on the ship, but we clearly see them throughout the rest of the movie. However, physics are arbitrary in the Locker.
If Barbossa started off as Jack Sparrow's first mate, then he would not have been a pirate lord and would not have had one of the nine pieces of eight unless he took it from Jack Sparrow prior to marooning him on the island (referenced in the first POTC). However, it is shown that Jack Sparrow still has one of the nine pieces of eight. How did Barbossa, as a mutinous first mate to Jack Sparrow, become one of the pirate lords and have one of the nine pieces of eight?
The Endevour is a first rate ship of the line. This means that, despite her armament, she was quite slow (3-4 knots at the most). Yet, she somehow manages to catch up with vessels like the Black Pearl and the Flying Dutchman, regarded to be the fastest ones afloat.
During the maelstrom battle scene, when Will Turner swings on a rope from the Black Pearl to the Flying Dutchman, it's obvious that a stunt double actually swings from the rope then falls to the deck several feet behind Orlando Bloom who then rises into frame. The stunt double lands on the deck and the camera cuts to a close up of Orlando standing up. It is not one single take, but two.
When the British break into the Singapore hideout and the battle starts, one soldier stumbles over on a fallen table. The next shot, which is facing the soldiers, shows him falling over again from another angle. He also falls in the exact same manner, meaning they had two cameras filming the scene.
Near the end of the film, just before the Endeavour is sunk by the Flying Dutchman and the Black Pearl, we see a shot of the Endeavour from behind. A wake can clearly be seen, suggesting the ship is driven by a diesel engine. Not even steam engines were invented in the period when this film is meant to be set, neither did sailing ships create such a visible wake, since they did not travel as fast as modern ships.
Just before the Flying Dutchman was to go into battle, Calypso was stirring the clouds and Davy Jones gripped the hole where his heart once was. You can see under his tentacle beard that it is his real hand gripping his chest
While Jack is viewing the map to the Fountain of Youth, in the Straits of Florida it can be seen written "Ponce De Leon 1523." Although possibly just an example of poor records, De Leon first sailed to Florida in 1513 and died in 1521.
When Sao Feng is killed, Elizabeth's "hat" flies off. Her hair changes positions, from a lot of hair - almost all of it down - to a few small locks of it down. It continues to change in the next few scenes where the crew claims her captain and she is talking to Norrington.
Before Barbossa releases Calypso, you get a clear look at the bowl with the Pirate Lords' nine pieces of eight. However there is an extra piece of eight in the form of a ball of string making it that there are already eight of the nine pieces of eight when Jack and Elizabeth's pieces of eight have clearly not been added since the next shot is of Barbossa adding them.
When the main characters meet on a small island of sand and King Elizabeth trades Jack for Will, Davy Jones needs to stand in a barrel of water because it hasn't been 10 years since his last day on land. You can clearly see at least two buckets of water leading up to the barrel Jones is standing in, in one of the wide angle shots. So he simply walked from one barrel to the next.