Plot hole: The whole problem with the teleporter occurs when fly DNA is mixed in with Seth Brundle's DNA, starting his transformation into the Brundlefly. Brundle is on a hiding to nothing from the word go, and the fly is irrelevant. Humans are a walking talking mass of foreign DNA - we are host to one trillion bacteria all of which has a complete compliment of DNA, as do various tiny mites that live in our hair follicles and all sorts of single cell organisms in our gut. If the transporter serves to mix the DNA of all living creatures which are in the transporter pod at the time Brundle would turn into a half-man, half-bacteria. Incidentally, DNA from a bacteria, an amoeba or a hair follicle mite would be just as 'compatible' with human DNA as that from an insect. It's quite a simple chemical, really.
Other mistake: In the final scene of the movie, Megan starts a boat motor and uses the propeller to hit Jason in the face, who has been chained down underwater. But if Jason can only barely reach her foor from underwater, there's no way the boat propeller is underwater far enough to reach his face. (01:17:50)
Factual error: When the Delta Force lands on a beach, prior to their assault, their landing craft is lit up like a christmas tree. The commandos wear dark uniforms and have blackened their faces, but they also carry bright white ropes around their chests. Some of them are scuba-divers, wearing yellow oxygen-tanks. In short, in the real world they would have been spotted within minutes.
Continuity mistake: During Kevin Bacon's race with fellow messenger, the scenes shift back and forth from New York to San Francisco. In one city, he's on a fixed gear (no freewheel on back wheel) and when the race is taking place in the other city, he's riding a single-speed. Basically, the cityscape and bicycles switch from scene to scene.
Factual error: In an early scene, the high school science teacher produces a schematic diagram of the two nuclear bomb designs created by the Manhattan Project. He says, "Here are two designs based on plutonium." Actually, only the Fat Man bomb uses plutonium. The other, the Little Boy design, uses uranium.