Character mistake: In the Iraqi Desert, when the British soldiers speak of the casualties and losses, one of the British soldiers mentions the loss of the Belgian contingent and possible reinforcements, then makes a reference to the "Golan Straits"; there is no such place.
Suggested correction: "Golan Straits" is another word (albeit dated one) for the Goland Heights which is a region of Syria occupied by Israel.
The region in question has no straits, which is the point of the entry. And never would the term "Golan Strait" be used to identify a 1,800 sq km plateau. The actor, or writer, used the wrong term that a soldier in that situation wouldn't use.
Revealing mistake: In the exterior shot of Air Force One and its accompanying jets in the air, just before the shot of David getting nauseous aboard Air Force One, something suddenly comes up along the entire bottom edge of the screen. This is only visible on fullscreen DVD. (01:08:10)
Suggested correction: That is another jet guarding Air Force One.
Factual error: Aliens are using TV satellites for their secret attack signal, making the TV picture quality poor. David shows the president how they do it by bypassing the curvature of the earth. However TV satellites don't work that way. They are "hanging" pretty much above their broadcasting area totally reflecting and spreading the signal back straight downward to earth. Turning the parabolic mirrors of the satellites to a different elevation would result in no TV signal on earth, not just a degraded one.
Suggested correction: Satellites do both. They both send the signals back down to earth but they also send signals to each other in order for the signal to cross the globe. And in those signals the aliens have hidden their own signal, and that distorts all satellite signals, causing TV's to receive a distorted signal.
Very few satellites directly talk to other satellites. Geosynchronous communication satellites don't. The antennas used for transmitting the TV signal are directional, but while directional antennas send most of their energy in one (or a few) direction, they still leak at least some energy to all directions, so it could still theoretically be used as described. The real mistake though is the aliens have advanced technology, so could easily have deployed a couple satellites of their own to perform this function, so why the need to use ones from Earth? Worst case just send a couple small ships up to act as relays.
It probably saves them time to use the satellites already in orbit. They are on a tight schedule and don't want to waste time and resources deploying their own satellites. Plus it's a small possibility for them that humans can take out their satellites, so hiding it in their own seems perfect.
They could be using the human satellites to disrupt communications or make communicating across the globe difficult to hinder any possible pre-emptive strike by Earth's armies acting in unison while the harvesters position themselves for the first wave of attack.
Continuity mistake: The alien saucer that arrives over Los Angeles is said to be approaching off the California coastline, yet it is specifically shown approaching from Imperial Valley, which is to the east/southeast of Los Angeles.
Suggested correction: Not true, Constance says, "One is heading for Los Angeles, the other two are on our eastern seaboard heading toward New York, and Washington D.C." No direction of travel is given.
General Grey reported to the President the destroyer (hidden in a fire cloud) was being tracked "off the California Coastline."
Other mistake: When David asks Major Mitchell if he can shoot the soda can, Major Mitchell has to ask a nearby sergeant for his sidearm, despite already having one on him when he shot the alien earlier.
Suggested correction: He probably shot his own gun empty or nearly empty, so he removed the magazine. They fired at least 10 shots at the alien, and he planted another 3 in it up close.