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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: 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.