Close to the end of the movie when Charlie Sheen wants to transmit the video from the control room, the power fails. He looks outside and sees an electricity cable has been cut. He then decides to go to the dish itself. Later on, the electricity in the control room works just fine.
When Zane hears that his former boss has been spreading lies about him and goes to NASA, the checkpoint guard sets a clipboard on the roof of his car. When he's refused entry, Zane angrily throws the car into reverse, and in the next shot, the clipboard is gone.
When Zane attempts to transmit the video from the control room, the power in the room fails due to a large cable being cut outside. However, the steel window curtain still rolls up when Zane presses a button, which would be impossible if there was no power in the room whatsoever.
Ilana tells Zane that the flower field she examined at the beginning of the film is 90 miles from the North Pole. Even if the ice pack melted, there would be no soil for plants to grow in, as the nearest land is more than 400 miles away.
Towards the end when Charlie and the girl run into a building, Charlie has a key to the deadbolt on the building door. But the deadbolt is installed wrong. It is a 'Kwikset' double cylinder deadbolt and the screws that hold it on the door are on the outside of the door, not the inside. Anyone with a screwdriver could simply remove the lock and open the door.
When Zane and Ilana are talking about the climate changes in San Marsol Zane has a flashback of the presentation that he had crashed earlier at JBL, however he should not have heard the part about the melting polar ice because he was already removed from the room by two security guards.