Revealing mistake: The man from Mars is in an elevator with a woman when the power goes out. He tells her he cut the electricity and gas powered engines all over the world for a half an hour. They proceed to show clips of the power out in different parts of the world. When they get to Big Ben in London, you can see a motorboat cruising down the river in the background. If the boat were powered by wood or coal, there would be plume of smoke trailing it. If it were powered by oil (ie. diesel) electricity is required to pump the fuel into the ejectors.
Revealing mistake: When the spaceship is going to take-off, every scientists are trying to escape, but there's a man wearing a light colored suit and hat who seems more interested in pushing the chairs everywhere than escaping. He even pushes a chair in another row. The director obviously told the actors to push some chairs to create more excitement in the scene, but he seems to take that too seriously.