When George and Linda drive away from Elysium the first time, there is paper and tape over the left rear side window of their car where it was damaged when it overturned. In the next shot, the paper and tape disappears and the window is undamaged. Then later, when you see the car in the lake the paper and tape is back again.
When Linda takes her clothes off in front of the bulldozer, the Atlanta PM camera crew are still not set up, but then on the TV they show the footage before she even begins to get naked.
After Linda shows her film to HBO, she angrily closes her laptop in the shot facing her. However, when we see the shot facing away from Linda ,you see the laptop is open again.
At the start of the film when George and Linda are speaking to the agent in the office, one scene shows children in the background on swings. Seconds later the same shot shows them missing.
When Seth is playing the guitar singing for Linda his hands are different than when he has stopped playing. In particular his thumb nail is longer while playing and than when stopped.
The "Deed" that is shown to us in the movie is titled "Deed of Trust". A warranty deed should have been used instead. A Deed of Trust does not give title to the property to the person buying the property, it gives title to a lender in trust to secure repayment of a loan used to buy the property.
When Linda presents her movie about Antarctica to HBO she makes reference to the Polar bears dying off. Polar bears do not live in Antarctica; they only live in the Arctic.
As George and Linda enter Atlanta for the first time, the cars are driving on the wrong side of the road. Traffic is on the left side. The film playback has been flipped mirror image wise.
As George drives the Escalade through the picnic tables of nudists, in one shot it is clearly not Paul Rudd driving.
The people at Elysium say that they don't clap because it's "too aggressive". But after they help George and Linda set their car upright, everyone claps.