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: In the scene at the start of the movie with the "authentic" piece of film, you can see a girl with a hat waving to the people at the ground. When the ship is leaving port in the film, she and others are in the same positions, only in reverse, because the first "authentic" shot is the same shot, only mirrored. (00:00:40 - 00:25:30)
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: Geologically, the type of volcano in the movie shouldn't erupt so much low-viscous magma; but due to make the volcano exciting to the audience, the movie makers probably deliberately ignored this mistake.
Deliberate mistake: Skylar's leaving is edited together with footage of Will sitting in a park watching planes take off - including, presumably, her plane. The sun is directly overhead in his scenes, while hers were filmed near sunset. (Most obvious when you see the very long shadows during the same airport footage which is also used in the deleted scene "Pudge Fisk Card"). (01:39:20)
Deliberate mistake: When Buddy's dog box falls out of the back of the truck the dog box is empty.
Deliberate mistake: The same shot of Odysseus killing a man with two swings of his sword is used twice in the battle scene.
Deliberate mistake: When they fight in the hangar and Troy is thrown back by the jet engine, his face and other parts of his body should have been burnt quite heavily. Such a jet engine has temperatures higher than 450°C about 5 meters away, and Troy is even closer than that.
Deliberate mistake: As Roper drives the Dodge into the shipyard watch the underside - no sign of McCall, even though he's visible under the body when he comes out of hiding.
Deliberate mistake: Throughout the whole short film, Geri's hair doesn't move or react to anything (such as the wind or his glasses). The glasses even seem to go through his hair without any movement in his hair. (00:01:00 - 00:03:35)