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?
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: During the scenes where Santos is working on the main engines, he is actually working on a generator. A tug of that size would have a set of much larger engines with reduction gears (transmission), or be hooked up to large electical power plant to provide propulsion.
Revealing mistake: When Epps is holding the detonator and it is knocked out of her hand, watch as it lands - when it hits the ground the trigger is pressed in yet there is no explosion.
Visible crew/equipment: When the tug leaves the harbour in search of the (ghost) ship you can see the waves of the ship from which the scene is being filmed.
Continuity mistake: In the scene right before Epps finds the little girl's skeleton hanging in the closet, she is seen walking down the hall looking for her. In one shot, she is wearing the heart locket; the same locket she finds on the dead girl minutes later.
Continuity mistake: When the demon meets the crew in a bar and asks them to find the lost ship he saw from the air, notice the beer bottles on the table; they keep changing from full to half full to full again, mainly the foam at the top.
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.
Visible crew/equipment: Julianna enters a large hall while exploring the ship by pushing two big glass doors open. Looking at Julianna coming in, you can see a movie-lightbar reflecting in the glass on the right.
Factual error: There were absolutely no signs of ice or frost in any scenes while they were in the Bering Strait.
Revealing mistake: In the beginning of the movie where the line cuts the dancers in half, blood is visible on the dress of one of the dancers before the line cuts her. This is best viewed in slow motion on the DVD.
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"
Deliberate mistake: If the captain is bending over the girl to protect her and the line is at about mouth height for him, the line couldn't have gone straight through his mouth. Instead, it would have run from the back of his lower jaw up and horizontally to his left eye.
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.