Factual error: The Skycrane helicopters have a max takeoff weight of 42,000 lbs. With them weighing in at 19,200 lbs, that leaves 22,800 lbs that they could lift. Even small carracks, the ships, weigh around 180,000 lbs.
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.
Other mistake: When Nate and Sully first meet Chloe in Barcelona, Chloe steals the cross from Nate. In none of the shots is Chloe's arm reaching anywhere. And the backpack never appears to be jostled. (00:33:45)
Continuity mistake: In the fight scene on the boat in the air - the cabin door is smashed in by Sully and "bad guy", but a shot later, Nate slams into the reappeared cabin door which is not smashed. (01:33:51)
Factual error: Nate and the other chick find four amphoras full of salt inside an ancient Roman storage room underneath Barcelona's streets. When they burst, the salt is released and spilt everywhere. Salt is a very hygroscopic mineral. It is impossible for that salt stored underneath the city's streets in a non-sealed container to not be one giant block of wet, melted solid after 500 years of humidity. It happens to kitchen salt if not stored in a dry place, let alone salt from the 16th century.
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.
Other mistake: Sully climbs up the helicopter chain in the final scene with a bag full of gold. Assuming modest dimensions of 30x30x30 cm for his backpack, that means that he was carrying at least 40 kilograms of gold on his back, but he tosses it around like it's full of fluff. And when he hits Braddock in the face with it later, he's tossing 40 kilos of gold at high velocity at her face, but she shows up later without a scratch.
Continuity mistake: When Sam leaves Nate at the orphanage, there's an orange lamp to the right side of the window emitting light on Sam's face. As it's on the right of Sam, the right side of his face should be lit orange; however, in the cut to the close-up, the orange light is on the left of Sam's face. This is likely due to the editor flipping the shot in post.
Other mistake: Sully jumps off the plane with the map but somehow Nate and Chloe end up with it.
Factual error: When Jo kills Santiago by slitting his throat, there is only a trickle of blood. He should be covered in it. This was probably done to keep the PG-13 rating.
Factual error: When they were in the underground chamber and it was filling up with water. Nate is still talking to Sully through his phone app, despite his phone being in his pocket which would make the call so muffled as to be inaudible.
Factual error: When Nathan and Chloe are freefalling from the plane, they're able to communicate with each other. This is physically impossible. They're probably falling at a speed of 120 mph a second, which would literally suck the air from your lungs if you tried talking at the altitude they fell out of the plane from.
Revealing mistake: During the scene with the ships hanging from the helicopters, Nate decides to fire a cannonball at the other helicopter as it's coming towards them. A standard cannonball shot from a 36 pound cannon that the Spanish used on their ships weighs 16.5 kilograms (the weight of a large full water dispenser bottle) but Nate tosses it around like it weighs nothing.
Continuity mistake: When Nathan gets out of the trunk of the red car in the cargo plane he is not wearing his ring necklace for a couple of scenes. Then it appears.