Factual error: The electrical power grid fails, depicted by a series of shots of city blackouts and equipment shutdowns. When the power goes out, the lights of an oil refinery go out as well as the flare. In actuality the exact opposite happens to a flare when powered equipment such as compressors and cooling devices fail simultaneously. The flare is not an electrically powered device and is designed to stay lit during power outages. All excess pressure is immediately vented to the flare stack within a second, causing an enormous flame and smoke cloud that will be visible for several miles.
Factual error: As Klaatu is walking down the train platform at Newark Penn Station, in the background you can see signs that say "VIA". VIA is the national railway of Canada and does not have a presence in New Jersey. This scene was filmed in Canada, as evidenced by the signs on the platform and the 1950s style streamlined passenger cars on the track. Neither Amtrak nor NJ Transit uses those type of cars in their trains.
Revealing mistake: When the guys are seen piloting the UAV's, they are using Saitek X52 Pro joysticks. These are commercially available controllers for Microsoft Flight Simulator. These were obviously used as props. Even if the army did use these for some reason, they weren't turned on in the movie (the buttons glow green when turned on).
Polygraph Operator: I'm going to ask you a series of control questions. Are you currently in a seated position?
Polygraph Operator: Are you human?
Klaatu: My body is.
Polygraph Operator: Do you feel pain?
Klaatu: My body does.
Polygraph Operator: Are you aware of an impending attack on the planet earth?
Klaatu: You should let me go.
Question: When Klaatu and Professor Barnhardt are writing on the black board together, are they solving something that we just haven't solved yet, and so answering this question is hopeless, or does anybody know what it is they are supposedly solving, it looks to be something to do with an event horizon.