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.
Factual error: Gorillas are strict herbivores. So why does Isabelle eat a rat at the beginning of the film? The serum may have turned her into a crazed killer, as it does with Sebastian, but it hasn't changed the structure of her teeth and palate, biochemistry of her digestive system and so on, all of which would be required. She might kill or torture the rat, but she'd never eat it.
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.
Other mistake: Elisabeth Shue uses the blowtorch to set off the fire sprinkler in the hallway, but later there is a raging inferno in the lab with all the important data and equipment and there's not one sprinkler, nor any alternative "electronic equipment friendly" automated fire suppression mechanism such as Halon gas.
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.
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.