Continuity mistake: Toward the end, Carmen Ibanez gets stabbed through the shoulder when she is brought before the big master alien thing. If you were to sustain such an injury, there would be so much swelling, not to mention just destroyed tissue, that you wouldn't be able to move that arm for weeks. Yet a few minutes later, she is seen hefting around a very large assault rifle, and seems to have no difficulty. I guess it's a pretty standard action movie "heroes can temporarily ignore injury in order to save the day" kind of oversight, but it just seems exaggerated in this case, considering how severe the shoulder trauma looked.
Continuity mistake: As the Roger Young is breaking up, the ship's captain is running from the bridge and falls down with the large door descending and striking her midriff. As it hits, she spews blood from her mouth against the side of the door in a arching/sweeping motion. When Carmen returns to help free her, the blood is not displayed in the same pattern, more concentrated to one area as opposed to swept.
Continuity mistake: In the scene where Rico is first in boot camp and Dizz says she is being transferred to the unit, she gets ready to fight the drill sergeant. She drops her papers, her jacket, and her bag. It cuts away for a few seconds, then goes back to the drill sergeant and Dizz in fighting stance. The piece of paper is farther back than before, this can be overlooked because of wind, perhaps. But the jacket and bag are both gone.
Continuity mistake: In the scene where Rico is getting ready to go to the end of school party, he puts on his black jacket and for a brief moment, we can see the collar is turned up at the back. During the following conversation with his parents he never adjusts his collar, yet when he turns his back, the collar is neatly in place.
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.