Revealing mistake: When Snake and the others are running across the 69th Street bridge after the taxi is destroyed, Brain runs to his left, insisting that's the safe path. He gets blown up by a mine. We can see the bright lights of the FX spread out in front of him; the mine is exploding before he actually steps on it. (01:25:40)
Continuity mistake: When Snake enters the Duke's railcar to find the President, he throws a knife at a guard's forehead. As the camera comes to the knife hitting him, we see a blood trail already on his face from that wound, before he could start bleeding. (00:59:30)
Other mistake: At the end of the movie, when the President puts the cassette tape into the player, the printed text is upside down on the player. The model is a Sanyo MT4200, which was an unusual unit; it had a TV on the side, and the dual cassettes on the top. But as we see his hand 'drop' the tape in, it must be on its side - there is no reason for it to be on its side, and no reason for the cameraman not to have turned it around so the text was right-side-up. (01:34:00)
Continuity mistake: When the President shoots the Duke with the machine gun from the wall, the first stream of bullets rips up the Duke, as we see multiple exit holes through his torso. The President lets loose another stream, and yet another - but just after the 3rd stream, the camera changes to the Duke, alive and without the holes just ripped through him, only to be 'killed' by this 3rd stream (where we also see the blood pack the actor is wearing). (01:29:45)
Continuity mistake: When the taxi crosses the bridge and gets split in two by the mine, the front half does a 180-degree turn and the rear half continues straight. The camera angle changes, and the front half is now going straight, and the rear half turns and slides to a sideways position. (01:24:50)
Continuity mistake: When Snake first rescues the President from the Duke's railcar, the two of them walk beside the train. They walk the whole length of car #2205, then they walk it again. The 'new' car has some graffiti on it; either the filmmakers used both sides of the car, or added the graffiti to make it look different, but they forgot to change/erase the car's big yellow numbers. (01:00:10)
Continuity mistake: When Snake, Brain and Maggie drive down Broadway, away from Brain's place where the Duke is, a number of people are attacking the car as it drives. Without anyone running down the street with the car, we see a group of people twice, possibly more. Easiest to notice are 3 specific guys in the same position beside each other at both locations. (00:56:15)
Factual error: When Air Force One crashes into the office building, the security force monitors show the escape pod falling to the ground - inside the building. Normal physics would dictate that the pod would 'slide' across the floor of the building it crashed into, not smash through 20 floors towards the ground. We can assume the buildings are in disrepair, but it has only been 11 years since the island was turned into a prison. (00:12:30)
Character mistake: When the revolutionary fighter commandeers Air Force One (we only know this once she's in control), a Secret Service agent is trying to break down the cockpit door by banging it with the butt of his automatic rifle. The way he's hitting the door, he couldn't break through a cereal box - it's much too weak. Presumably, the actor is taking it easy on the door because it's a cheap prop door. (00:11:15)
Plot hole: When Snake, Brain, Maggie, and the President get to the car at the WTC, Snake opens the hood when the car is dead, and somehow he is out in the open when the Duke is about to shoot. First, how would he get there with a crossbow trained on him, and second, how did Maggie pass the revolver to him, when he hands it to her to open the hood of the car? (01:21:05 - 01:21:50)
Suggested correction: When the hood is opened Maggie can be seen immediately putting the revolver behind her back. Being stood very close to Snake it's assumed it was passed to him offscreen. With the crossbow trained on Snake the Duke monologues directly to Snake allowing him to step a foot or so away from the car to look like he's listening and going to accept his capture but ultimately it was to have a shot at the steam engine and create a distraction. Maggie took out the crossbow guy by slamming the hood on him.