Plot hole: The 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.
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: The elevator to enter the lab requires a visible-light thumb scan, but Caine enters the lab (and apparently not by following someone) after he has become invisible. A fingerprint is not sufficient for the type of scanner shown. The gloves he wears would also not follow the contours of his fingertips closely enough to copy his fingerprints.
Plot hole: Caine's skin becomes visible when it chars, for no reason consistent with the other invisibility. Further, it drops off in an impossible way (since there's no indication the invisibility otherwise changes metabolism/healing). Caine acts far too healthy for someone so severely burned. Finally, the extreme damage to skin and muscles that this implies is not seen when he becomes visible. (Even if the material flaking off is clothing, most of the arguments still apply; burned clothing would adhere to burned skin, and would provide little to no protection from the fire.).