Deliberate mistake: At the beginning and especially at the end, Julianna Margulies spends extensive time in the ocean, wearing nothing but cargo pants and a T-shirt. Considering the movie takes place just off the Bering Strait, wouldn't she have quickly frozen to death? (01:21:05)
Revealing mistake: When the crew are getting ready to load up the gold, one of the crew slams the crate lid making the gold bars "move".
Plot hole: The crew of the Antonia Graza is shown blowing off the door to where the gold is by putting an explosive on the INSIDE of the door. What was the purpose of blowing off a door AFTER going inside the door, planting the explosive, then going back out?
Factual error: Murphy tells the story of the "Mary Celeste" all wrong. As this is a real incident, from real life, there would be no need for him to make anything up or tell it as a "tall tale", and as a professional salvage expert he would be familiar with it. The "Mary Celeste" was carrying 1700 barrels of denatured alcohol, not cotton, like he says. And she did not sail into the Mediterranean on her own to be found off Tripoli, but was discovered straight on course in the Atlantic, despite having been abandoned for some time (according to the last log entry). See http://www.straightdope.com/mailbag/mmaryceleste.html for more details.
Factual error: In the opening scene, when all the people are cut in half, one man's top half falls off his body taking his spinal cord with him from the bottom half. Surely this would have been cut in half along with the rest of his body.
Plot hole: Ships only steer when moving 'through' the water, not while adrift (moving 'with' the water/current). So the whole idea of fixing the rudder to steer away from the rocks without any propulsion is nonsense.
Factual error: The wire which cuts the dancing characters in half severs their torsos in a neat line a few inches below their armpits - but their arms remain intact. They should have been severed too, a few inches below the shoulder, and should fall away from their bodies separately.
Suggested correction: The dancers for the most part have their arms extended roughly horizontally around their partner, hence the wire generally passing below and leaving them attached.
Factual error: When they have discovered the gold aboard the Antonia Graza, Murphy is asked how much it is worth. He says that it might be worth 200 or 300 million (dollars). A fine ounce of gold (31.04 grams) goes for $360; thus, a kilogram of gold costs about $11,000. There are seven crates of gold. Since every single one of those can be handled by two men, they can't weigh more than, say, 150 kgs (and that's probably pushing it). Thus, the maximum amount of gold would be one ton (approximately). Given the aforementioned gold price, that'd be about 11 million dollars. Still respectable, but nowhere near the figure Murphy mentions.
Factual error: Maritime law states that you are given a percentage of whatever you find, not the entire amount of whatever you find.
Continuity mistake: When Francesca is messing with Greer, his shirt says "Everlast" on it. After he falls down the shaft, the word is gone.
Continuity mistake: When Francesca is hanging by her neck, in the background we see the guy she killed laying on the floor. His body disappears then reappears in different shots.
Plot hole: After the tugboat is sunk, the crew try to repair a very old ocean liner - the ghost ship - using equipment that could only have come from the tugboat, which had the latest scuba gear and welding gear, but they are all at the bottom of the ocean in the blown-up tugboat.
Suggested correction: The salvage crew are shown very early on bringing a variety of equipment onto the liner long before their own ship is sunk. It is obviously intended to insinuate where the salvage gear required later came from.
Continuity mistake: When Francesca is half-nude, she turns to walk around the far side of the glass enclosure. The camera cuts in closer, and she begins her turn again.
Factual error: When Murphy goes into the "Cabina de Capitano" (Captain's Cabin), he sees the glass with a little alcohol in it, and the bottle standing next to it, without a cork or stopper. If left standing open like that, after 40 years, the liquid would have evaporated. However, it can be said that the Captain's ghost made it appear to entice Murphy.
Suggested correction: I think the captain's ghost did that just like Francesca had the lit cigarette inside the ash tray.
I amended my entry to reflect your suggestion, thank you.
