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.
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, as wouldn't all of the fur on the gorilla.
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.
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 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.
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.
Plot hole: Where does Sebastian come from in the end when he grabs Elizabeth Shue? We would have seen him if he was on top of the elevator and he surely could not have been hiding in the fire.
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: 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: Rats have very poor eyesight but an extremely keen sense of smell. (see www.pestproducts.com/norway) 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.
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.
Continuity mistake: Sometimes you can see the outline of Kevin Bacon's head, when he is running to the toilet to puke, for example.
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.
Continuity mistake: When they first inject Kevin Bacon with the stuff that makes him invisible, he thrashes around in pain. He lunges to his left breaking the strap holding down his right arm. In the scenes that follow his right arm is still strapped in. They even unstrap him to let him up.
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.).
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.