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: 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: 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.