Plot hole: The idea that Ben Gates had to run away despite the President's being okay with the kidnapping does not make sense. The President could simply pardon him if necessary. However, when he ran away, he would likely be committing other crimes (fleeing and eluding police, reckless driving, etc.) that would not be federal crimes and so would not be pardonable.
Suggested correction: That's basically what he did at the end. Even though the President was OK with Ben "kidnapping" him, if Ben didn't find the lost city of gold he would have been arrested and charged for kidnapping the President (amongst other charges). However, because Ben was able to find the city the President gave him and his crew a full pardon and explained that it was a misunderstanding.
Plot hole: In order for the treasure trail to be followed both desks would need to have existed in 1865 when the code was deciphered. However HMS Resolute wasn't broken up and made into desks until 1879.
Suggested correction: In the movie, the code-written in the 1860s-leads to Laboulaye's lady, which was already conceptualised in 1865. The statue, which was theoretically inscribed after the Resolute wreck was made into desks, then points to them.
Factual error: When the group comes to Mount Rushmore, they arrive at a lake. There is no lake close to Mount Rushmore (look at Google Maps, the lake used is Sylvan Lake, which is a good 15 miles away from Mount Rushmore). Mount Rushmore is suppose to be a "cover up" for the final treasure and that would make the chamber underneath the faces itself. (01:27:05)
Suggested correction: The story-line states that Mt. Rushmore was created to hide the clues to the treasure, not hold the actual treasure.
But they climbed over Mt Rushmore to view the lake which is in a different direction.
