(at around 1h 3 mins) This film shows the compass being given to Jack by a captain he worked for in his youth as that captain is dying. In Pirates of the Caribbean: Dead Man's Chest (2006), Tia Dalma said he bartered the compass from her.
The bottle that the Black Pearl is in is a different bottle than the bottle it was in in Pirates of the Caribbean: On Stranger Tides (2011).
When Carina is running away from the guards her iron shackles are still visible, but when she is next seen in the clock maker's shop the shackles are gone, only to reappear in the next scene.
As Captain Sparrow is being forcibly married to the ugly woman on the beach, the vicar is facing the beach, and there is a crowd of onlookers. Yet Captain Barbosa and his crew managed to sail a huge ship up to the beach, disembark, and stride right up to the wedding party, without anyone noticing until he announces himself.
When the bank is being pulled through the town by the horse team there is a moment near the bridge where the horses are missing.
(at around 18 mins) The pulling ability of a team of large horses is nowhere near the force required to pull a building along dry ground.
The zombie sharks shows ribs through the the decay holes on it's bodies, but sharks actually has no ribs or bones, only cartilage on it's head, spine and fins.
(at around 33 minutes) The glow from the blood moon allows Carina to find a clue in her diary. However, blood moons do not cast off red light. A blood moon is caused by a lunar eclipse. Because some sunlight reaches the moon indirectly, the moon can sometimes appear red in color. But it never actually shines red so a red glow filling the room is impossible.
(at around 35 mins) Jack still refers to Will as a eunuch. Of course Will is not a eunuch, as he managed to father a child. Jack referring to Will as eunuch is a recurring joke from the first movie, not to be taken seriously.
(at around 46 mins) The rope around Carina's neck is long enough for her to simply step off the trap door after the hangman has been knocked to the ground.
Living in the mid-18th century, Carina is wearing 19th century underwear when she swims to the island.
During the skirmish between the Black Pearl and the Silent Mary's crews, as the former ship gets boarded, Captain Barbossa is seen fighting with a Silent Mary Officer, and the both of them appear left-handed. This however results an error: Barbossa's dominant hand and peg leg would be ill positioned, and the same goes for the Spanish Officers and the features of his uniform.
The image has clearly been mistakenly flipped.
(at around 57 mins) The British commander demands a witch to interpret Carina's calculations on the prison cell wall. In reality, a naval commander of the 18th century - or any educated person at the time, in fact - would be quite familiar with such drawings. Carina's abilities shouldn't have been surprising to anyone, much less a sailor, as astronomy was a proven science and the British in particular very keen on its study. In fact, by the time the movie is set, the Greenwich Naval Observatory was over a century old. At the most, Carina would have been considered eccentric or a little odd, but never a witch.
Carina Smyth's trial and conviction for witchcraft is not realistic of the time period. The last execution for witchcraft in England was in 1716, with the Witchcraft Act of 1738 completely abolishing the practice in 1736 all over the British Empire. The movie is set in 1755.
(at around 19 mins) When Carina Smyth uses the telescope and the steward says: "No woman has ever handled my herschel". Wilhelm Herschel would have been 17 years of age in 1755. Wilhelm Herschel is famous for a new type of reflector, called herschel telescope, but visible telescope is a refractor.
(at around 1h 9 mins) There is no way that Carina Smyth would carry a pocket chronometer. Maritime chronometers were invented around 1761 though earlier attempts were made. But no chronometer could be carried in a hand. They were large instruments in a gimbal mount in a wooden box.
(at around 43 mins) As Jack mentions the guillotine as a form of execution, he says it is French and mentions that they also invented mayonnaise. While he is right, the guillotine was given its name and current appearance (particularly the angled blade shown in the movie) by Dr. Joseph Guillotin in 1789. While a previous version was already available in England at the time the movie is set (1750's), it was called a "maiden", and had a curved or straight blade. Also, mayonnaise sauce, though previous versions were known, was not given that name until 1806.
(at around 14 mins) The first scenes take place on the island of Saint Martin that appears to be under English rule. This is historically inaccurate for Saint Martin has been under Dutch and French rule since the mid 17th century. This movie is set in the mid 18th century.
When the crew leave Jack after the bank job, they walk along the beach in front of the docked ship where there is an island visible in the background. When they release the ship into the sea later, there is nothing but open blue ocean expanse surrounding them and no island.
Jack the monkey is still cursed from Cortez's gold, as seen in every previous film, yet is shown in the moonlight without his cursed appearance.
It is said that Salazar leaves one man alive to tell the tale, but during the first battle he kills the captain of the ship and only finds out Turner is below deck when he trips over a bucket. This means Salazar didn't know anyone else was on board when he killed the captain.
Salazar is released from the Devils triangle because Jack gives away the compass. However he had previously given the compass to Will Turner in "At World's End" before throwing Will overboard to be picked up by Cutler Beckett and Davey Jones.
Salazar tells Barbossa that he and his crew hunt and destroy only Pirate ships. Yet they attack and destroy British naval ships as well.
In Dead Man's Chest and At World's End, it is mentioned multiple times that the Flying Dutchman MUST have a Captain to ferry souls to the other side. However, when Will is freed from the curse at the end of this film, this supposedly important fact is completely forgotten about.
(at around 1h 28 mins) Carina says she is named after "the brightest star of the North". This is wrong for several reasons. Carina is not a star, but a constellation. Carina is located in the Southern hemisphere; in fact it can't even be seen in most of the Northern hemisphere. The movie takes place in 1755, and Carina wasn't named until 1763, having been an integral part of the larger Argo Navis constellation. The brightest star, not just in the Northern hemisphere but the entire visible galaxy, is Sirius (the "dog star").
In Dead Man's Chest, it's revealed that Tia Dalma was the one who gave Jack his magic compass. But in this film he is shown receiving it from a dying crew mate during his initial encounter with Salazar.
When the sailors give young Captain Jack their tribute, one of them gives him the string of beads he always wears on his bandanna. But At World's End revealed that this was one of the Pieces of Eight that designated pirate captains. Additionally, those Pieces of Eight came from the original captains that bound Calypso. Jack Sparrow should have gotten this from the captain, designating him the new captain.
Captain Salazar and his men are Spanish. Yet they sometimes speak among themselves in English.
Captain Salazar's claims: "I would tell him myself, but Dead Men tell no tales".
But he says this, after telling a complete story, in other words: he already told a tale.