During the data heist, the fan cooling Kruger's armor is missing several blades. In later scenes, no blades are missing.
When Kruger initially deploys his shield against Max, he drops his sword, which is red with blood. When he picks it up afterwards, the blade is clean and shiny.
When Kruger is sitting next to Frey on board the Raven, he is wearing his armor. When he walks over to the control console a few seconds later, his armor is gone.
SECDEF Delacourt is wearing a white-on-white suit at the pool party when she receives the communication about an illegal ship approaching. In the next scene, she is walking to a control room wearing a metallic gray suit. The transit time from Earth is cited as 19 minutes, so it is unlikely she would have changed so fast. From the control room, she is urgently summoned by the President and appears in front of him wearing the white suit again.
Although Max's augmentation is bolted directly to his body, he later is shown wearing a t-shirt underneath.
The original "Stanford Torus" design of a wheel-shaped space colony had an offset mirror angled to reflect sunlight onto mirrors set around the central hub and then outward to the ring. Elysium has no such arrangement and sunlight simply shines directly to the interior of the ring. This is completely impractical, as Elysium rotates (about every 6 minutes). This means that location around the habitat would have an ongoing series of periods of "day" and "night", each lasting only 3 minutes, which would be extremely disconcerting for the inhabitants. In addition, Elysium appears to have its rotational axis pointing towards the Earth, and as it orbits the Earth that would mean that (a) it rotates with respect to the Sun, and so the amount of sunlight and its angle will be continuously varying, and (b) during each orbit it will spend time in the Earth's shadow and not receive any sunlight at all.
When Max and Julio's car is attacked by the delayed-detonation RPG's launched from Kruger's ship, the attack angle and detonation are contradictory to the laws of physics. Since Max and Julio were traveling backwards, the explosive force of the two devices would have lifted the car from the front end backwards, not from the rear end forwards as shown.
When the little girl with crutches is smuggled onto Elysium, the medical scanner diagnoses "multiple compound fractures". However, a compound fracture (modernly called an open fracture) is where broken bones cut through the skin. There were no such injuries on the girl as she walked with her crutches.
A Stanford torus, such as Elysium, would be too small to be visible in the sky of Los Angeles to the naked eye in the daylight. Comets and asteroids which are orders of magnitude brighter than Elysium could ever be, are not visible in space to unaided human sight.
After being struck by Kruger's missile, Max escapes his overturned car by gripping the door with his fingers and bending it open. Max's fingers are not augmented like the rest of his body. He would not have been able to grip the door as shown and bend it open without severe injury to his hand.
Elysium is shown several times not to have a solid roof. However, this would mean that, despite the rather slow rotation imparted to create the effects of gravity, the atmosphere would have very quickly escaped to space. However, Kruger has an energy shield that blocks bullets. Something similar could keep in the air at Elysium.
The opening title at 58 seconds says, "In the late 21st century Earth was diseased, polluted and vastly overpopulated", but later it is revealed the current year is 2154 which is the 22nd century. This is not a goof as it is stating the problems began in the 21st century and they clearly continued through 2154.
Elysium computer detected Delacourt dying, yet did not detect her life threatening injury or alert anyone to send medical aid. Since her brain was undamaged she could simply be healed as Krueger was.
Max wearing his exosuit performs heavy muscle activities clearly indicate that he is not supported by his exosuit at all. The scene where he pulls open the lock of the chair in the crashed vehicle he hangs with a single hand in a bowed position clearly using only his muscle strength to hold him in position.
Every time an 'illegal' from earth wants to enter a house on Elysium they are shown having to break a window or door to gain access. However, in such a perfect, i.e. want free (and, incidentally. heavily monitored) society there would be no need for locks on any home.
When Kruger fires the missiles at the ships heading towards the Elysium it shows him fire four missiles, yet only a few minutes later there are only three missiles (one for each ship).
How in the heck is he wearing a shirt after the exoskeleton surgery? It's not on him on the table when their drilling into his back and attaching the hardware.
There are numerous changes in Delacourt's dialog that are clearly visible after Max and Frey are on Elysium. She says "Get these two out of here." while looking at Frey and her daughter but she clearly says something else. You can hear the difference between the lines that are changed and those that aren't.
When Max's alarm clock goes off on the morning of his accident, a robotic voice announces the time is 5.50am, however, the digital readout clearly reads 6.00.
When Kruger radios Delacourt to tell her that he is en route to Elysium and she replies that she will expect him to arrive in 19 minutes, her words do not match what she is saying.
When Max gets trapped in the droid chamber and suffers a lethal dose of radiation, the procedure stops immediately when the system detects organic tissue in the chamber. Even by today's strict industrial security standards, the human worker should have been recognized BEFORE the chamber was fired up and the sequence would not have initiated at all.
Lethal radiation poisoning occurs due to the destruction of cellular DNA inside the subject's body. The absence of functioning DNA leaves the cells unable to replicate, and death quickly follows due to lethal infection or collapse of critical organ systems as their cells die off.
Max suffers a total body irradiation sufficient to be lethal within five days, but is able to undergo a traumatic and non-sterile surgery to implant an exoskeleton and neural device inside the brain without any ill effects. The total absence of a functioning immune system and wound healing mechanisms would have assuredly killed or at least incapacitated Max soon after the surgery.
The robotic parole officer has the sensory capabilities to detect vital signs but is unable to detect when people are writing graffiti on it.
With the wondrous technology on Elysium and its ability to detect the approach of unauthorized shuttles, one would expect some sort of automated missile system to deter or destroy interlopers.
Shuttles are allowed to land directly on the surface, when it would be much safer to have a landing port on the outside with suitable security.
As simple a system as a few barrage balloons and strung wires would prevent illegal landings (and so spoil the script, of course).
As simple a system as a few barrage balloons and strung wires would prevent illegal landings (and so spoil the script, of course).