Plot hole: Sam sent a post card from the church where the keys are used. But Sam was captured moments after locating the book that gives the clue about the church, and would never have had a chance to go there.
Plot hole: The hero had to dive to get in to the cave where the wrecks are but the baddies can just drive in with their boats.
Plot hole: There's no way more or all of the passages/rooms going out from beneath the church had been discovered as the surroundings has gone through examination and conservation throughout the years.
Plot hole: Nate did not have his postcards from his brother with him when he got out of the car on the plane and certainly not when he was jettisoned from the plane. If the answer to this they were in his pockets, the falling from the plane, fighting, and being in the sea would have meant they were mangled, lost or extremely wet and mainly destroyed. Yet he and Chloe have them along with the map that Sully exited the plane with (another mistake someone else mentioned), as if they had arrived yesterday.
Answer: Jo and her mercenaries were at the wrong island, It's when they saw Drake go past them in a speed boat, and not to the island they were on, that's when they realised they had been tricked.