Plot hole: Bond makes a huge tactical error after diving to the St. Georges. He knows the Russians and their operatives are after the ATAC. The ATAC itself is expendable to Britain, since it has a self-destruct mechanism that, under proper procedure, would have been set off when the ship sank. So why is Bond trying to retrieve it? Because he disarms the self-destruct, he actually allows Kristatos to get his hands on it, forcing Bond to track it down again and, to stop the Russians from getting it, HE DESTROYS IT! So why doesn't Bond, instead of disarming the self-destruct, set a timed charge or toss a grenade in the room to destroy the ATAC while it's at the bottom of the sea? The answer is, of course, that if Bond destroys the ATAC before the bad guys can get at it, the movie's over. Even so, at the end, when Bond finally does destroy the ATAC, he tells Gogol it's "detente. You don't have it. I don't have it." Clever line, but it reinforces the fact that the British don't need it. They can build another one.
Plot hole: When Indy and Sallah visit the gentleman who translates the staff headpiece for them we hear the staff should be "six cadams high." Indy replies, "About 72 inches." Then, turning the headpiece over, "Wait - take back one cadam to honor the Hebrew God whose ark this is." It's definitely referring to the staff length - Indy says afterwards "Their staff is too long." So, about five feet now, right? But, when Indy goes to the map room the staff is much taller than him. If the staff is about five feet high, Indy would be around three feet tall. (00:48:25 - 00:53:05)
Plot hole: Mr. Foyt spies on J.J. and Victor to find out more about the Cannonball, yet fails to recognize them when they stop to pick him up.
Plot hole: In the scene where Colby is discussing tactics with the team, Pele interrupts and takes the chalk from Colby and says "Hatch gives me the ball here, I do this, this, this, this, goal" while drawing a line on the blackboard to indicate dribbling from one end of the pitch to the other. At that point in the film, Hatch was only the trainer, not the goalkeeper.
Plot hole: Max drives from the hillside to the crashed car to save the occupants but the guy with the crossbow doing up his boots somehow doesn't hear Max's V8 engine approaching, or hear Max get out and sneak up on him, this area would be quiet and Max must have parked nearby to get the injured man to his car.
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.