Elysium is an awesome movie. It's worth seeing. A sci-fi spectacle with Matt Damon, Jodie Foster, William Fichtner, and lots of blood splatter. What more do you want?
Like most such movies, of course, it has a fundamental flaw that completely undermines its premise. It makes heroes of the wrong side.
The real villain of this story isn't Elysium; it's a lack of population control. The real hero aren't the people of Earth; it's life-saving technology.
The movie's naive conclusion is that, when all the billions of people on Earth are made citizens of Elysium, the life-saving technology miraculously becomes available to all.
This is not how things work. When a resource is only available to a few people, it's usually because it's scarce. What makes a resource scarce usually isn't a decree from government, but a law of nature that we have not yet learned how to overcome. In order for a major new technology to become more cheaply available to more people, scientific and technological breakthroughs are needed. If you don't solve the scientific and/or technological bottlenecks, the resource remains scarce, regardless of legislation.
So the movie, really, is depressing. The protagonist helped prolong the lives of many people; but his effect on the world's population had to have been negligible, and ultimately disappointing, because the life-saving technology of Elysium would not be available in sufficient quantity to help more than a fraction of people on Earth. If it were, the technology would not have been restricted to Elysium in the first place.
Meanwhile, the real tragedy is no population control, and it continues unresolved at the end of the movie.