The biggest issue I have is the program that Matt Damon ("Max") carries around in his head for about 2/3 of the movie. When the executive guy uploads the program to his brain, he copy-protects it such that unauthorized copying of the thing will kill whoever's got it in his brain. That's fine, because one would presume he has the password (or whatever) required to unlock the copy protection.
There's the scene where Spider hooks Max up to his computers and rifles through the data copied from the executive dude's brain. Why didn't that kill Max? I mean, Spider's downloading the program; it's an unauthorized access and the fact that he could see the program means it's being downloaded from Max's brain. That should have killed him.
Further, why did the unauthorized upload from the executive dude not kill Max? What's the point of a copy-protected program that lets you copy it once?
The entire movie was meant to be an allegorical tale about illegal immigration; Earth is Mexico (which is why Max's native language was Spanish) and Elysium is the United States (which is why Jodie Foster's thugbots were "Homeland Security"). (Also, Jodie Foster was seriously evocative of Hillary Clinton, BTW.)
Then there's the economics. Robotics are prevalent and sophisticated enough that the police are machines, and in fact much of the justice system is mechanical. Max's parole agent is a machine that would probably fail a Turing test, but it would not fail it by much--not when it was capable of evaluating a sarcastic statement and assigning a high probability to the statement being sarcastic and/or abusive.
Why do people have to work at all with that kind of machine intelligence? At that level of sophistication, people can sit around drinking mai tais and watching television while the machines do all the work. Everyone on Earth ought to be rich beyond dreams of avarice rather than living in an endless barrio.
Further: the big draw for people trying to get to Elysium illegally comes from the magical, mystical medical machines they have there. I am hardly exaggerating: an unremarkable example of this machine cures a little girl of end-stage terminal leukemia in about thirty seconds, and another rebuilds a man's face in perhaps twenty seconds after he took a grenade blast to the head. Each house in Elysium has such a machine.
Given robotic labor (not free but extremely cheap) and mass production, why aren't there billions of these things littering the planet?
The economics of the world presented by the movie simply do not make any sense whatsoever. What it amounts to is the rich people of Elysium keeping all the good stuff to themselves because they're big meany mean-heads.
At the beginning of the movie, Matt Damon tells us, gravely, that Earth became too overcrowded and diseased, so the rich people took all their money into space and built Elysium.
...apparently out of pixie dust and unicorn flatus, because otherwise they would have had to spend a shitton of money on Earth to get people and materials up into orbit where Elysium was being built. It would have required investment in infrastructure and labor to make the thing happen. (Perhaps the money itself was their building material.) And spending all that money on Earth would have done wonders for the planetary economy.
"Overcrowded and diseased" would inevitably take care of itself, in the absence of decent medical technology, and pretty quickly to boot. The Four Horsemen are always ready to ride--but if you run the numbers you learn that the entire population of Earth in 2014 would fit comfortably in a land area no larger than Texas, and have plenty of elbow room to boot; and populations only expand asymptotically in poor areas. Give people other leisure options beside procreation and their birth rates decline.
Still, the world presented in the movie is totalitarian. Max gets his arm broken by a robo-cop when he makes a wisecrack about his knapsack being full of hair-care products (he shaves his head). (Hmm, a robot which has enough AI to be insulted by a smartass, and break his arm in retaliation. Tell me again why people have to work?) The parole officer-bot unilaterally decides that Max will spend more time on parole for his "abusive behavior" (ie the wisecrack he made to the robo-cop).
And if the world is totalitarian, then that explains why everyone on Earth is dirt poor.
(Not explained: why the executive dude has to have his factory on Earth, manned by human labor. Why not have it on the Moon or somewhere, staffed entirely by robots? Labor is the single largest cost of nearly any conventional business, so if you can replace people with machines--)
What happens at the end? Of course, Spider runs the program in Max's brain (killing Max) and everyone on Earth suddenly becomes a citizen of Elysium, and therefore entitled to the magical medical care. Hundreds of medical shuttles are dispatched to Earth, crewed by robots and full of the magical medical machines. The grand liberal dream of socialized medicine comes true at last!
Not shown: the riots that would ensue, because all too many people would refuse to wait their turns. There wouldn't be orderly lines of people waiting patiently for their turns in the machines; the rioting would make the Watts Riot look like a birthday party and it would happen everywhere one of those shuttles touched down.
To say nothing of people who would decide, "If I have that shuttle I will own this town!" and try to seize control of the things. You know?
And then, what happens some ten, fifteen, twenty, forty years down the line, when no one on Earth is dying any more? Because the machines in charge of Elysium were told that everyone was a citizen and entitled to perfect medical care?
"Overcrowded" doesn't even begin to cover it. Then you'd really see the Four Horsemen ride--oh, "Pestilence" would remain home because the magic medical machines would eradicate disease, but Famine and War would have a field day.
Ultimately, to make the movie work, you have to ignore human nature and most of the laws of economics.
"People on Earth are so poor because of automation! Robots terk der jerbs!" ...and why, then, is any product costly enough to be worth rationing?
Remember the example of AOL software CDs. In the 1990s AOL practically carpet-bombed peoples' mailboxes with their client software on CDs, trying to get people to sign up for Internet access through them. How many billions of CDs do you think AOL had pressed? What do you think it cost them, per CD, to press and mail those CDs?
If AOL paid more than $0.10 per CD--in those quantities!--they were suckered.
...because manufacturing CDs is cheap. Done correctly the entire process can be automated; the basic raw materials are a simple polycarbonate plastic, stamped out by a press, and coated with the barest whisper of vaporized aluminum. (One aluminum beverage can is probably enough to make about a thousand CDs.)
If things are made by automated machine--if making them requires little or no human intervention--they can be made so cheaply that the mind boggles. Consider the ordinary incandescent light bulb; if you really think about it, it's a marvel: a tungsten wire suspended in high vacuum inside a glass globe, all made so cheaply that a store can make a profit on a four-pack sold for a dollar.
Because you don't have to pay a machine. It never takes a sick day, never needs a vacation, never develops alcoholism or cancer. It just keeps running until it breaks or runs out of raw materials--and if you only need to employ people to fix the machines that break, whatever you manufacture will be cheap even as you make money hand over fist.
The kind of judgement displayed by the robots in Elysium--the kind required to be halfway effective police!--indicates that they're more than capable of replacing humans in basic manufacturing jobs.
There should be no poverty in that world. None.
But of course the movie was made in Hollywood, and the tropes of the world portrayed had to obey all the political preferences of the Hollywood elites, and that's why Elysium doesn't work at all as science fiction. It works splendidly as a shoot-'em-up movie, and it's entertaining, but it's just not SF.