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.
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.
Factual error: When we first see Caine (Bacon) enter the military base, there are Willy's Jeeps used by military personnel. By the year 2000, the Willy's Jeep was long-since replaced in the U.S. Military by the HUMVEE, which we also see in the film.
Suggested correction: It's not a Willy's jeep. It's a Ford M151 Mutt, which was still in occasional use at the time of filming.
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.