Revealing mistake: When Rico jumps on to the back of the tanker alien and starts shooting at its back, you can see the outline on the back of the tanker that is going to be shot up before Rico starts shooting.
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.
Visible crew/equipment: When Rico gets thrown from the tanker bug and lands on his back on the ground, a piece of the flap covering the mattress pops up.
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.
Continuity mistake: Regarding Lt. Rasczak - in the scene where he is teaching his students, you can see his left arm where it was previously amputated, and how close it is to the elbow joint. But later in the movie, when he is introduced to Diz, Rico, and Ace in the Roughnecks, you can see that his arm is much longer than where the amputation from the previous scene would have been, even with the "implant" hand that he now has.
Factual error: The last thing Rico's parents say before the meteor strikes is, "Looks like rain," as the sky outside gets darker. As a large meteor (large enough to destroy a major city) makes it's appearance in the atmosphere, there would be a flash of light brighter than the sun. Several minutes later a dark dust cloud would rise, but by then everyone in the vicinity would be killed.
Plot hole: A Bug meteor knocks out the Roger Young's communications. She dodged it at sublight maneuvering speeds, indicating that it is moving fairly slowly. If it is so important that she warn Earth it's coming (which is how we know their comm was damaged), why doesn't she jump back to tell them or destroy it herself? Even if she has no capital ship weapons (she is a troop carrier), there is no indication that her faster jump drive is damaged or needs longer than they have to warn Earth to charge for a jump, or that she can't leave her patrol station, etc.
Other mistake: When Shujumi has the lower half of his leg cut off by a warrior bug, no blood comes out.
Revealing mistake: During the last play of the football game, Dizzy throws Rico the ball and he does an impressive flying flip over several players. Right before the flip, it's extremely obvious that Rico runs up an off camera ramp/stairway in order to perform this flip.
Revealing mistake: Just before Dizzy gets skewered by a warrior bug, you can see breakaway panels on her body armor at the points where the CGI bug impales her, to cover the squibs used to make the holes. The shot is already shown in slow-mo so it's easy to spot.
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.
Continuity mistake: In the scene when Dizzy says she is being transferred to the unit and she gets ready to fight the drill sergeant, the sun changes between shots.