Norrington's orders are signed George R, which was King George I's signature, which would date the time period between 1714-1727.
Port is used to describe the left side of a ship (specifically, "drop the port anchor"). Until the 19th century, "larboard" was still used when referring to the actual side. Port was used for direction, i.e. "Hard a' port" or "Port helm".
When Barbossa reveals the curse, one of the pirates on the capstan has a concertina. The concertina wasn't invented until 1829.
"Scallywag" is used to describe a fellow pirate. Scallywag was invented after The American Civil War (1861-1865), and referred to white southerners who collaborated in the Reconstruction.
Jack uses the phrase "Bob's your uncle", meaning everything is taken care of. It refers to Prime Minister Lord Robert Salisbury, who appointed his nephew Secretary of Ireland in the 1890s.
The Interceptor and Dauntless are painted in Nelson Chequer — black and yellow bands with black gunports. This scheme first appeared on the HMS Victory in 1803, and subsequently painted on the rest of Admiral Nelson's ships, but did not become widespread until after Trafalgar in 1805.
The Interceptor and Dauntless fly the Blue Ensign. Before 1864, the colour of an ensign denoted the ship's station. Blue denotes Pacific, Atlantic and East Indies. The Red Ensign denotes the West Indies and the Mediterranean.
The very American phrase "Off limits" is used, instead of the more appropriate British "Out of bounds".
The rank of Commodore was not a substantative rank until 1996. Before then, a Post-Captain would be appointed Commodore of a squadron. He would relinquish this command when the posting/mission ended or if an Admiral arrived. Further, an Admiral commanded the West Indies station, not a Commodore.
Royal Navy officers are wearing uniforms not introduced until 1747.
The Dauntless in the opening bears the Coat of Arms of King William III, who reigned from 1689 to 1702.
Jamaica's capitol and the governor's mansion is in Port Royal, which was completely destroyed by an earthquake in 1692, after which it was moved to Spanish Town.
Barbossa's Granny Smith apples originated in Austrailia in 1868.
The Dauntless has at least one carronade in the opening. The carronade was not invented until at least 1759, and not implimented until 1779, and only became commonplace in the 1790s.
The Dauntless, a 104 gun first rate, is stationed in the West Indies. No ship that size was stationed there, for several reason: First rates required large crews — the Victory, on which the Dauntless is based, had a crew of 850+ — which would be very susceptible to tropical diseases and difficult to replenish quickly, were maintenance intensive, were limited in range since there were exactly two dry docks in the entire British Empire that could accomodate a first rate, one in Portsmouth, the other in India (though technically owned by the Honourable East India Company, but accessible to the Royal Navy), and were too deep drafted to be of much use in the West Indies. Further, the Royal Navy only had six first rates in service at the time.
Jack's gold false teeth are an interesting example: they are loosely possible (at least one surgeon in France was fitting silver teeth in this period, though it's unlikely a pirate in the tropics would have access to his services), but the dentures are a bit too good: all false teeth were not fitted very securely and wearers usually had to take them out to eat. Jack certainly shouldn't be able to eat apples without cutting them (and they'd probably come out when he gets slapped)
17th-century curled wigs, 18th-century panniered skirts, 19th-century teacups and, strangely, the young Elizabeth saying "okay"! Elizabeth's corset, while women wore garments that looked like that, would have been technologically impossible to tie so tight it made her ill (no whaleboning yet and without steel eyelets the lace-holes would have torn when she sat down). Oh, and Port Royal was destroyed in an earthquake in 1692 (and subsequently rebuilt, but not as the bustling metropolis seen in the movies). And it wasn't a clean, proper little English town. (A deleted scene reveals their Port Royal is only civilized from the sheltered, upper-class perspective.)
Dead Man's Chest
Lord Cutler Beckett's flagship HMS Endeavour.
At World's End
Singapore didn't exist at that time, it was founded in 1819.
There's a Teddy Bear at the end. The incident with Theodore Roosevelt and his bear took place in November 1902. The political cartoons of Clifford Berryman which were inspired by the incident started appearing that month. The toy bears inspired by the cartoon were introduced, simultaneously but independently, by Morris Michtom and Richard Steiff in 1903.
On Stranger Tides
This movie has Jack Sparrow interacting with two historical characters: King George II and Blackbeard. Edward Teach, the historical Blackbeard, died in 1718. George II didn't become King until 1727 and the movie has him appearing to be much older than the 44 years he was in 1727 (he's portrayed by Richard Griffiths who was 63).
The movie also has Blackbeard, who died at around the age of 38, being played by the 68 year old Ian McShane.
It should be noted that Jack referred to Blackbeard's real life death, or more specifically his beheading after the Battle of Ocracoke Island. Backstory explains Blackbeard surviving by bribing Robert Maynard (the man who killed him in real life) into claiming that he slew Blackbeard and took his head.
The Union Flag is the current version incorporating the red saltire of Saint Patrick's flag representing Ireland. This first flew in 1801 following the Act of Union 1800.
Made a bigger slip up considering the previous films used the correct rendition of the Union Flag (the one lacking the Saint Patrick's cross).
They use the Blue Ensign, which denotes Atlantic, Pacific and East Indies stations. The correct flag would be the Red Ensign, which denotes West Indies.
Also it features Blackbeard as a pirate and Barbossa as a British privateer. Blackbeard didn't become a pirate until after Britain outlawed the practice of privateering.