Plot hole: When Bridgette ran through the glass and Linda and Jim were at the hospital Jim tells Linda he called her mom and told her what happened and she was coming to stay over the next day. Yet apparently her mom forgot what happened because she had her committed because Linda didn't remember what happened to Bridgette's face. Also, Bridgette was like 9. How come no-one just asked her what happened?
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: Turner locks himself and Ashley in her car so he can confront her. However after his speech, Turner somehow manages to open the door without unlocking it.
Suggested correction: It is accurate that Turner can open the door without unlocking it, all modern cars can be opened from the inside whether the door is locked or not. Ashley never actually tries to open the door, she reaches for the handle and stops once Turner locks the door. Since the movie never actually shows Ashley try to open the door, this doesn't count as a plot hole. If anything this is a character mistake, Ashley should be well aware that she can't be "locked in" a car that new.
Plot hole: Landy uses the code 4/15/71 to point Bourne to the training site address. But how does he know it is on the East side?
Plot hole: When Agent Memphis is about to be executed they ask him if he needs to "Piss" so as to not have government-used drugs in his system before he commits suicide. They even mention writing a suicide note for him. He's had seven shades beaten out of him though and was kidnapped whilst on the phone, mid-conversation and with possible witnesses. Surely if it wasn't the first time they had done this then they would have taken more care to make sure it wasn't a complete fake-out.
Plot hole: When Detective Broussard is killed and Patrick was being interviewed by police (dressed in a white shirt), the interviewing police detective say "a couple of nights ago you were at the quarry." In fact it was months before when they were trying negotiate the release of Amanda at the quarry. It unravels the entire movie.
Plot hole: *SPOILER* Toward the end of the movie, Ryan Gosling goes to Hopkins' house where Hopkins is tricked into not only confessing again, but giving Gosling the murder weapon, after they are back in court and Gosling is the acting prosecutor. This would be a conflict of interest due to the fact that Gosling is a witness.
Suggested correction: First, the gun that Beachum took from Crowford's house was not the murder weapon. It was Crowford's unfired gun. He only took it out of the fear of his life. Second, Beachum entered Crowford's house with police supervision. If he plays it by the book, Crowford's confession is valid. In that case, supervising officers will stand witness, along with a recording confirming their testimony. Third, Beachum doesn't need the confession anymore. He was amply clear on that matter.