Plot hole: Why on earth would the military be interested in a soldier (sailor, aviator, whatever) who has to go into combat naked and unarmed, and who is detectable by an enemy equipped with a pair of cheap, mass-produced goggles? How would you treat them if they were injured? They would be utterly useless in any form of military operation, even espionage.
Plot hole: Peter goes into Carl's mind to save Catherine. When he's in there he sees the tank with the water nymph. On the tank are strange symbols which provide the FBI with the clue needed to find the latest victim. Makes sense so far. But, go back to the scene just after the FBI have captured the comatose killer and are looking in his basement. The FBI are looking at the contraption that the killer uses to suspend himself over the victim. On the contraption is the same symbol seen later on the water nymph's tank. Why didn't the FBI follow up the symbol then?
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: When Tim Robbins is floating away in space his wife could have easily saved him. She could go out a little further, use the grappler to catch her husband, then use the fuel she has remaining to halt their acceleration towards the planet and return them partway to the necessary orbital altitude/velocity to rendezvous with the resupply module. Then, Gary Sinise could come out partway to them using his thrusters, Connie could shoot the grappler out to him, and he could reel both Connie and Tim Robbins back in to the resupply module.
Plot hole: After Nanahara and Noriko run away from Akamatsu at the school, Niida shows up from behind some bushes opposite the school and inadvertently kills Akamatsu with his crossbow. But Niida is Boy 16, which means he should still be in the school building (he's supposed to come out after Noriko, who's Girl 15). There's no way he has any time to get into those bushes.
Plot hole: When Captain Towers gives his XO an injection to allow him to die in peace, he, properly, swabs the site with alcohol, and slips the needle into the vein. However, immediately below the injection site, is a hep-lock.a port installed into a vein to allow injectables to be administered. I cannot imagine that a senior Naval officer would be so ignorant of the port's function.
Plot hole: How did Carolyn Fry get out of the cave in the canyon to confront Riddick at the Skiff? Riddick strained to roll the rock into the cave entrance, and he was a big, strong man from a position of good leverage. How did Carolyn and the other two push the rock out of the way so that Carolyn could get out? And, then, how did Carolyn mange to push the rock back into place? It was still there when she and Riddick came back from the Skiff to bring back the other two.
Suggested correction: Presumably the military are interested because Sebastian's research could lead to advanced forms of invisibility technology, such as the ability to turn materials and weapons invisible for use in combat.
You cannot second guess the film like that. Sebastian is making no effort to make non-living items invisible and throughout the film we see that is not possible (why else would Sebastian have to walk about naked?). His research is on animals (and later humans) not "materials and weapons" and is based on their physiology, anatomy and metabolism. How would you inject a rifle or a tank with a serum? They don't have a bloodstream. The military wouldn't see any value at all in this research - maybe they would be interested in invisibility, but not if it was restricted to living creatures as we see here.
You know how easy it would be for an invisible person to infiltrate an enemy's compound undetected and take out powerful leaders or dictators? Especially if no-one knew the technology existed.
Easy? Impossible. First, they would be naked and unarmed. Too bad if you are trying to knock off Vladimir Putin - a taekwondo black belt - with your bare hands during a Moscow winter! Being invisible doesn't mean you can avoid making a sound or triggering a pressure plate or an infrared detector and so on and so on. Final answer - a naked, unarmed combatant would be about as useful as a chocolate teapot in any form of operation, covert or otherwise.