Crew or equipment visible: The support Quentin is standing on is visible just before Kazan drops in.
Revealing mistakes: When Kazan lowers himself into the blue sound-activated trap room, the set cube wobbles from left to right enough to spoil the illusion (though only for about two seconds) that the cube is solid, inflexible metal.
Continuity: When Quentin drops Holloway, the "clothes rope" is still hanging from the door, under Quentin, and held by the others in the room. But after the cutaway, the rope has disappeared.
Continuity: Quentin beats Worth brutally with a boot, clearly ready to kill him or at least to knock him out. However, Worth stands up again with only one bruise under his right eye, a single scratch, and a stream of blood running from his ear. These are what Star Trek fans call "tasteful wounds," referring to Captain Kirk frequently receiving a thin slice of blood across the cheekbone, chest, or shoulder.
Errors made by characters (possibly deliberate errors by the filmmakers): Leaven claims that the problem of finding factors or primes is astronomical. This is ridiculous. It is very easy to determine if a 3-digit number is prime. The largest factor you have to check is 31, and 2, 3, 5, 7 and 11 are all very easy to check, leaving only 6 factors to check. In addition, powers of primes for 3-digit numbers are MUCH easier to check: there are only 11 primes that have squares, only 4 that have cubes, and higher than this there are only powers of 2 and 3, and those are trivial. In short, the calculations should be simple. Not astronomical.
Continuity: Leaven cracks a lens on her glasses in the beginning of the film. However, during some shots, the crack in the lens is missing.