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.
When Leaven first checks the rooms' set of numbers for primes, she has to think for a few seconds for each set. The first set of numbers she checks ends in 5; the second set ends in 2. Numbers ending in 2 or 5 (other than 2 and 5 themselves) by definition cannot be prime. Someone proficient at math, as Leaven is, wouldn't need to think about the numbers; she'd register they were multiples of 2 and 5 and move straight to the last number.
Kazan is supposed to be a math genius, something that the plot hinges on, but he makes several mistakes when calculating the number of prime factors to find out whether a room is trapped or not. He says that 462 has three prime factors, when it has four, that 206 has four when it only has two and that 563 has two and 911 has three when both are actually prime numbers.
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.
Throughout the movie they are told to suck on the buttons from their shirts. In one scene, once Holloway climbs into the next room, Quentin is sucking on his button. He immediately speaks to Worth, muddling some words because of the button in his mouth. All of a sudden, the button disappears from his mouth and is in his hand again, and he then puts it back into his mouth.
When Leaven figured out that adding up the digits in the numbers gave her their coordinates in the cube, she would have almost immediately noticed that the coordinates were not in sequence from one room to the next (since the rooms were shifting).
After you enter a new room, the chamber doors automatically spin their handles and close shut. There is a scene near the end where Quentin closes a chamber door himself while another character is talking. The director admits in the commentary that this is because that particular shot was done earlier in the filming before he decided they would close automatically.
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.
The goof item below may give away important plot points.
Incorrectly regarded as goofs
When Alderson enters the last chamber and starts to walk forward, his arms are at his sides. However, after the mesh hits him, his right hand falls to pieces and is shown to be perpendicular to his body. However, right before you hear the "swoosh" of the mesh, you see his arms move off from his sides, making this possible.