Factual error: Amongst the essential parts of a nuclear weapon's detonation mechanism is a radioactive isotope of tritium, which has a half life of just 12 1/2 years. The tritium in every nuke on earth has to be replaced every ten years or so. This is by no means unusual; there are other perishable parts including detonators made of conventional explosives which would be completely inert after a thousand years. After lying dormant with no maintenance at all for that amount of time the nuclear weapons the 'Man-animals' find would be big shiny paperweights and not much else.
Factual error: The cavemen Harrier pilots are shown using the hover mode frequently. Harriers, even with drop tanks as depicted in the film, can hover for at most 5-10 minutes, as the thrust required to keep the aircraft in the air without any lift consumes massive amounts of fuel and overheats the engine, and real-life Harrier pilots are instructed never to hover for long periods of time, unless absolutely necessary. The amount of time the cavemen spent hovering (hiding out of sight in a parking garage, sneaking up on the Psychlo gunships, etc.) would have easily caused their fuel to run dry.
Plot hole: The facilities at Ft. Hood have working electricity to power the simulators, projectors, etc. even though it's been 1000 years, with no logical reason for the Psychlos to have kept the facility maintained, and the fact that the Psychlos should by rights have leveled the place when they invaded 1000 years before. Even automatic backup generators would have no fuel after 1000 years dormancy except for a nuclear system, which would still have required regular maintenance over a 1000 year interval to maintain automatic functionality.
Plot hole: After 1000 years have passed (without any maintenance) the Harrier jets still function like new. Amazing.
Factual error: The tyres, rubber and plastic gaskets, belt drives, upholstery, in fact all non-metallic parts of the thousand year old jeeps, aircraft, generators and so on found by the 'Man-animals' would have crumbled to dust well within the thousand years they have been sitting around before they are discovered.
Factual error: During the revolt, Carlo (Kim Coates) is attacked by several Psychlo gunships on the dome's roof. He then uses a Carl Gustav recoilless rifle to destroy one of them. Strangely, the missile he fires is heat seeking, evidenced by it missing the target and arcing back around to strike the gunship from behind. Carl Gustavs are not designed to fire heat seeking missiles, as they lack the tracking systems necessary to do so, since the weapon is an anti-tank rifle in real life. (01:30:55)
Plot hole: The barbarians find a working 1000 year old flight simulator. Beside the fact that the machine should not be working to begin with after such time, they were lucky enough to find a working power source in the barren wasteland.
Factual error: We see the nuclear weapon used to destroy the planet Psychlo pulled out of a cruise missile. A warhead cannot be yanked out of the missile and detonated without the fissionable material being removed and built into an entirely new device. This a safeguard to keep them from being pulled out and used in exactly this way.
Revealing mistake: When Jonny is running away from Terl in the mall at the start of the film, he goes through several panes of glass, smashing through them. One of them breaks up before he hits it.
Factual error: The main character and several others take a Psychlo ship and head for Washington, DC, where they land in front of a building with a dome, with "Library of Congress" spelled out above the building's entrance. The Library of Congress does not have a dome like the one depicted, in real life. The building they landed near is actually the Capitol Building, evidenced by the building's design and the distinctive dome shape. The Library of Congress is housed in three buildings, none of which match the depiction in the film. Humanity has been enslaved since the year 2000, so they would hardly have been in a position to move or remodel a library. (01:12:15)
Plot hole: Terl says that the army of humanity (presumably the U.S. Army) could only put up a nine minute fight against the Psychlos, and yet in the end of the film, a couple of outsiders, who taught themselves everything they know in just two weeks, can defeat their army. Why? The outsiders are outnumbered, they have had zero combat-experience, they use weapons that are over a thousand years old. That's just amazing.
Chosen answer: It is residual radiation from atomic weapons used in an attempt to fight off the Psychlos.