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.
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.
Trivia: John Travolta made the film with Franchise Pictures. A few years after the film, it was revealed in a court case that Franchise had fraudulently overstated the budget of Battlefield Earth by $21 million to scam investors. After losing the case, Franchise filed for bankruptcy, and Travolta fired his manager, who set up the deal with Franchise in the first place.