Factual error: The meteor that hits Buenos Aires was fired from Klendathu, a planet that, per the galactic chart shown after the hit, to be a third of the way around the galaxy. That the crew of the Roger Young had time to detect it and avoid it means it was not traveling at any kind of hyper velocity. It means it would have had to have been fired from Klendathu millions of years previously. That is some long range planning.
Suggested correction: Not an error, although it's never explained how it's possible to have a near real time war over relativistic distances. We definitely see that the Earth forces can respond to events in 'bug-space' by communicating and sending ships. That the bugs are also doing this is logical.
Continuity mistake: When Rico is typing on the computer to find out his math score, the close up shot of him typing on the keyboard shows a black long sleeve which changes back to a rolled up green button up shirt after he's done typing.
Other mistake: When Shujumi has the lower half of his leg cut off by a warrior bug, no blood comes out.
Continuity mistake: During the defense of Whiskey Outpost, as the Roughnecks fall back into the compound, one trooper is struck in the back by a bug. To his left there is only one trooper on the platform, but as he is hit, two troopers jump down.
Continuity mistake: When Ace jumps the line at the M.I cafeteria and is confronted by Rico, Zim moves in from behind for a closer look but arrives at the same position twice.
Continuity mistake: When Dizzy fights with the sergeant, the position of the soldiers in the background changes between shots.