Deliberate mistake: Elizabeth Shue uses a drawer handle as an electromagnet. OK if it's really a magnetic material but lab furniture is generally made of aluminium or stainless steel which is not. There is no way that they would use an iron handle in a potentially wet, and hence corrosive, environment such as a freezer.
Deliberate mistake: When Sebastian goes to his employer's house to kill him, the man is standing by his pool smoking a cigarette. When the boss blows smoke in Sebastian's direction, Sebastian appears and scares him. Since Sebastian is invisible you shouldn't be able to see his pupils, only an outline of his eyeballs, but you can see the pupils.
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.