Deliberate mistake: Leaven spends too much time thinking about if 645 and 372 are prime numbers to be believable. But she knows the factors of 649 and the result of 26 to the power of 3 almost immediately. Plus anyone with any maths knowledge whatsoever would know that any even number (or one divisible by 5) can't be prime, so 645 and 372 could be dismissed without even thinking about it.
Deliberate mistake: When the ship crashes into the dock, all of the scenes leading up to the crash and after it show a clear view across the harbor as we can see lights and land on the other side. It's not until the ship is about to crash that a thick and dense fog appears and disappears within a minute to mask the ship to create a more dramatic effect.
Deliberate mistake: Every time Nicholas enters his gate at home, it's daylight and then when he drives up to the house it is night. Either he has a 300 mile property or there is something else going on. It would appear that it is deliberate as it happens many times in the film. Symbolically, Nick is leaving the world as he appears with wealth and privilege (light) and entering the real van Orton world of solitude and sadness (dark). (00:09:00 - 00:09:55)
Deliberate mistake: The slow rate of the radio telescopes at the VLA has been greatly increased for the movie. They are actually quite slow and make little to no noise.
Deliberate mistake: In a lot of the shots in the cockpit, when Teri is attempting to begin taking control of the aircraft, notice the Horizontal Situation Indicator on the First Officer's side. The compass rose is moving around erratically - which would suggest that the 747 is also changing heading extremely erratically and robotically - which isn't possible.
Deliberate mistake: When Sonya finishes Mileena, Mileena's shoulders are muddy and she is face down, but when we have a close up of the dragon tattoo the right shoulder is cleaned off and what mud is left is dry. (00:42:25)
Deliberate mistake: When White almost fights with Exley in the street and is pulled away, the public mailbox by the side of the road is all blue. Mailboxes back then were red on top and blue on the bottom.
Deliberate mistake: When Barbara Wilson/Batgirl first arrives she is standing on a ledge beside the front door when Robin answers the door. She then exclaims, "Oh. Uncle Alfred." However she could not possibly have seen him, not just because of her angle, but also the fact it is after that statement that he first comes into view. (00:34:10)
Deliberate mistake: When Margo is in the Superstition exhibit, she thinks she hears/sees something and runs for her life. She gets into the women's bathroom and tries catching her breath before the mirror. Hearing a noise outside of the bathroom, she goes into a stall, locks the door, and stands up on the toilet so her feet don't touch the floor. It was just a little old maid washing her hands outside the stall, and the strange sound Margo heard was the maid using her inhaler. However, how is this little old lady - with asthma, we can assume - supposed to have gotten all the way from deep inside the exhibit to the women's room within seconds, pushing a big heavy cart? Why would she even be in such a hurry? We can assume, however, that perhaps this was a deliberate mistake to show that, after all, maybe Margo wasn't just freaking out over nothing...that perhaps something was in the exhibit with her.
Deliberate mistake: This mistake/trick was revealed in the second DVD commentary on the film. When Bond is underwater in the ship with the flare, this flare does not behave realistically. If they had used real flares, it would have put too much smoke and dirt in the water and quickly made it too murky to see or film through. So the flare used was a special effects prop of a bright light with bubbles being fed through it to give a good effect, but is not how a real flare would be under water. (01:08:25)
Deliberate mistake: Declan and Preston are hanging out at an airfield in a blue car when they realise one of the numbers in the notebook they have is an FBI access code that The Jackal now has. In establishing shot of this scene you see the blue car sitting more towards the left with Declan on the hood. Then when Preston calls in this finding and they get a helicopter to come pick them up, in the shot with the chopper coming the car is now suddenly much further to the right. It seems they had to move it during filming to allow a place for the chopper to land. (01:19:05 - 01:20:30)