Factual error: The gold bars that the crew finds must be some new type of light weight gold. There's no way that Julianna could stuff a gold bar in her back pocket and then pull it out and toss it on the table and Greer simply tosses it back and forth like it was plastic. A gold bar weighs around 27 pounds, you definitely wouldn't be tossing it around.
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.
Continuity mistake: When Jack ask Sean if he can talk to him alone for a minute, you see Jack lift his hand up pointing back with his thumb. Then he lowers his hand again. When it cuts you see Jack still holding his hand up. You also see Epps reaching in her pocket with her right hand, and when it cuts she is suddenly holding a cracker.
Continuity mistake: In the beginning, when the crew is dividing their money, the number of beer bottles on the table increases between the shots. At first, there are a few half full bottles. Suddenly, there are a few full bottles and a few empty bottles, with no time to have drunk them.
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.
Visible crew/equipment: At the beginning right before Santos sees the Graza, the Arctic Warrior is traveling on the sea. Off to the left you can make out the shape of another ship. Now why would that ship not have shown up on radar when Santos had said that the radar blip he saw was "10 miles to the NE"? (NOTE: you might have to kick your tv's video settings up a few notches in order to see this mistake but it is there plain as day.).
Factual error: The Italian words/phrases that can be seen on the ship doors, billboards, etc. are very badly translated. In particular, the phrase "Veleno di attenzione" in the flashback part, in English would sound like "Poison of Attention." The correct Italian translation would be "Attenzione: Veleno"
xx:xx:xxMarcus CaptainSlow Belicchi
Continuity mistake: In the scene where Epps is looking at the swimming pool, when she falls backwards from seeing Katie at the top of the stairs, there is a safety ring at the bottom of the pool. Yet later on in the film when Katie is showing Epps what happened to the people in the ship and how people were shot in front of the pool, there is no ring.
Continuity mistake: In the scene where Francesca is seducing Greer she is standing at a shaft. She is holding her hand at a door post. Each time the camera looks from behind her her hand is somwhere slightly above her head. When the camera looks from the other side her hand is much lower, at the height of her neck.