'Curse of the Black Pearl' References

Governor Swann pulls a candlestick off the prison wall, mirroring Will pulling one off of the Governor's wall in the first film.

Jack asks "Why is the rum always gone?", and advises people to keep the rum away from Elizabeth. This mirrors a scene in the first film, in which Elizabeth destroyed a large cache of rum. At the time Sparrow, who had particularly enjoyed the rum, asked, "Why is the rum gone?" Later in the film, when Jack recognizes Elizabeth as one of the new crew signed on in Tortuga, he turns to a crewman and orders, "Hide the rum!"
Another reference to rum is during an attempt to repel the kraken; finding out there is no more gunpowder, Will gives the order to use the rum for the explosive device, which shocked all the pirates. After a brief moment of silence, Gibbs finally sobbed the order to place rum in it. Incidentally, the one that pulls the trigger on the gun to blow up this cache of rum is Jack, not Elizabeth.

Jack mentions being made a chief in the first film.

Jack refers to Will as being castrated (he asked Will if he was a eunuch in the first movie), and gestures this to the tribe of cannibals.

Barbossa's monkey, Jack, appears briefly as a skeleton, referencing an obscure scene following the credits in the first film.

Barbossa's desire to eat apples in the first film is finally completed as he takes a bite out of one before the end credits.

When Will asked a couple of women about Jack, only to end up being slapped in the face as Jack was three times before.

The prisoners calling something towards them through the prison bars, the dog with the keys in the first and Elizabeth in the second.

Jack tells Norrington that he's still rooting for him, alluding to the first film where he says he was rooting for him all along in his attempts to win Elizabeth's affection.

The dog with the keys had run off in the first and Governor Swann wants to know where it is now. It apparently has gone off with two of the pirates from the first movie and at a cameo at the end, we see that the natives have made it their chief.

Elizabeth pretends to faint when Norrington, Jack, and Will are in a sword fight to get their attention, whereas she fainted twice in the first movie. She faints for real at the start of the first movie and was consequently saved by Jack, and then pretended to faint later on, to distract the on-lookers (Norrington and the governor), allowing Will to help Jack escape from the gallows.

Will claims to have used two sea turtles strapped together in his escape from the Flying Dutchman, in the first film Gibbs claims Jack used this method to escape the small island he was marooned on.

The man who arrests Will and Elizabeth (Lord Cutler Beckett), played by Tom Hollander, refers to when he had an encounter with Jack before, while holding a branding iron. On it is the same symbol branded on Jack's right arm during the first movie when Norrington pulls up his sleeve.

Just before the crew makes their escape from the island where the Dead Man's Chest is buried, Jack hits Will over the head with an oar, knocking him out. Will did this same thing to Jack in the first film.

In the first film, Will mentions that they are trying to get to Isla de Muerta with a compass that "doesn't even point north." Gibbs replies, "But we're not trying to find north, are we?" which foreshadows the revelation that the compass points to the user's greatest desire in Dead Man's Chest.

Elisabeth says just before the end of 'Dead Man's Chest' that Jack is “a good man”. In 'Curse of the Black Pearl' it is Will Turner who says this about Jack.

The words "'Ello poppet" are in both movies. Both times it is Pintel who says it.

source: Wikipedia
And thanks to Robert H.