Deliberate mistake: The four main "good guy" characters are stuck on an island with people who are trying to kill them. Steven Baldwin's character brings a pistol and takes a machine gun from one of the bad guys. Several times they overcome other armed men, but after defeating them, never bother to take the bad guys' guns. At one point, two characters argue over who gets to carry the pistol, yet when they knock out a man armed with a rifle, they leave it with him and just walk away.
Plot hole: A tsunami has supposedly just hit the island, yet the trees and plants (and a 500 year old treasure chest) are undamaged.
Plot hole: The day after the plane crash-lands on the island, we see an aircraft carrier at sea and a squadron of heavily armed Marines climbing on board a Chinook helicopter. Someone is heard saying that they picked up a mayday from the plane before it went down, and the Marines are on their way to save the people on the island. Why did the Marines wait until the next day to go rescue the people? And if it's a rescue mission, why are they in full battle gear and carrying so many guns, since nothing was mentioned about the bad guys being on the island? These questions are moot since the Marines never arrive and no mention is ever made of them or the rescue mission again.
Factual error: The storm that causes the plane to crash has supposedly also created a tsunami, which is headed for the island that the main characters are on. They claim to have "four or five" hours until it arrives. First of all, tsunamis aren't caused by storms. Additionally, when the "tsunami" is shown out at sea, it appears as a giant wave that overturns a cruise ship. In reality, tsunamis don't crest like that until they get close to land. Out at sea, a tsunami can pass right under a ship and the passengers would never know it.
Factual error: When the good guys finally find Columbus' treasure, it's in a wooden chest sitting outside. It seems unlikely that it would have survived 500 years outdoors. Even if no one had discovered it, the wood would have disintegrated long ago.
Deliberate mistake: The map and overlay that lead everyone to the island are supposed to be over 500 years old. Yet they're in amazingly good shape and hold up very well considering how roughly they're handled.
Plot hole: When the plane is crash landing in the storm and Nicolette Sheridan is calling for 'mayday', they can't get through to anyone because of the weather. The next day, one of the characters claims they heard on the plane's radio (before they crashed) that there's a tsunami headed toward them. If the radio was out, how did they know about the tsunami?
Revealing mistake: When the main characters hide in the "cave" to escape the tsunami, it is obviously man-made. Notice the stripes in the wall behind Steven Baldwin, which are obviously made by mining equipment.