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: There must be a lot of dumb scientists in Sebastian's lab. While defibrillating the invisible gorilla, (s)he becomes completely visible for a moment. However, not once do the scientists consider that applying a mild electrical shock to the system renders the invisible animal visible again - that electricity may be the key to the whole invisibility problem. They don't even comment upon the fact that the gorilla does become visible.
Factual error: The serum is transported by blood. Hair has no blood traveling to it, only the root. So, unless Bacon shaved his body clean, his hair wouldn't have become invisible, likewise all of the fur on the gorilla.
Suggested correction: The serum could have been absorbed by the roots and made its way to the tip of the hair strands (similar to colored water going up a piece of celery, changing the color of the celery).
Mammal hair is not porous and is not subject to capillary action.
Continuity mistake: Why does the Twinkie Kevin Bacon eats disappear immediately? If things that go into him disappear, when they give the needle to the gorilla, you shouldn't see the needle point when it is stuck in her arm.
Factual error: Rats have very poor eyesight but an extremely keen sense of smell. The rat introduced into the gorilla's cage would know right away that there was another animal in the cage and would never scamper happily into danger, as this one does.
Continuity mistake: At the end of film when Elizabeth and her lover are escaping from Sebastian in the hall, Liz turned on the fire alarm and everything became wet. But after that, they, and their clothes, are dry.
Factual error: When they put the gorilla back into the cage in the movie, who is said to be female several times, you can spot that it has a silver back. Female gorillas do not ever have silver backs - it's strictly a male thing.
Continuity mistake: When they try to make Kevin visible, they use a blue spray to see his vein (like they did to the gorilla). but you never see the blue mark again...
Continuity mistake: When Elizabeth Shue and her boyfriend are locked in the freezer, the camera keeps cutting back to the thermometer which is visibly and rapidly moving downward. However, it doesn't seem to have moved at all while the camera is not on it.
Continuity mistake: When they're pouring the "goo" on Kevin Bacon to make the mask, some of it gets on the end of his breathing tube. When they change shots, it is clean again.
Factual error: At the end of the movie, Sebastian Caine tries to hit the girl and her lover, but misses and gets electrocuted. With that amount of water on the floor, all three of them would get electrocuted.
Factual error: When the crew pour liquid latex over Sebastian's head and neck, in order to create a fairly life-like mask of his face, it simply pours over his head as though he is completely bald, and he is able to remove it later by pulling it off, exactly like a glove. However, the film creators seem to forget that Sebastian has quite a thick head of hair, and technically, when they pour the latex over his head, it should stick and/or pour along the outline of his hair. Whilst drying, the mask should equally have stuck to his hair and become very difficult to remove, and yet as they create the mask, no hair appears to exist on Sebastian's head. They did not shave Sebastian's head - later in the film he falls into a swimming pool and we see a clear outline of his entire body, with a full head of hair. (00:47:15 - 00:48:30)
Continuity mistake: When the veterinary is throwing blood to stain Sebastian, she stains her left breast. A few seconds after, there's no stain.
Continuity mistake: Sometimes you can see the outline of Kevin Bacon's head, when he is running to the toilet to puke, for example.
Continuity mistake: When the gorilla is lying on the bed, you can't see any marks on the mattress, but when they make Kevin Bacon invisible you can see his shape marked on it.
Factual error: During the scene in which Sebastian is chasing Elizabeth Shue and her boyfriend up the ladder in the elevator shaft, not only would the heat from the fire burn them, they would have all suffocated as the long-burning explosion quickly consumed their oxygen.
Factual error: When they inject the serum that counters the invisibility into the gorilla, you see the serum flow backwards toward the gorilla's hand. Veins have special valves that prevent blood flow from going backwards and to force blood to go to the heart, so how the serum manages this is beyond me.
Factual error: When they make the gorilla visible again, her heart becomes audible at the same time it becomes visible. This happens with Kevin Bacon as well. But that shouldn't happen, because it was just invisible, not inaudible. And it wouldn't make a noise like that unless you were listening through a stethoscope.
Continuity mistake: At the beginning of the film, a phone conversation tells us that it will be morning soon and Kevin Bacon will meet them at the lab first thing in the morning. Yet when they show the car driving on the highway to the lab, all of the shadows are straight down.
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.