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 complement 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.
Plot hole: In any given volume of air, there are any number of tiny, living organisms; dust mites, viruses, bacteria, etc. Why did the teleporter combine Seth's DNA only with the fly that was in the chamber? If he had taken the "floating organisms" into account in his calculations and programming, then why would he not have excluded ALL foreign DNA?
Revealing mistake: In the scene where Ronnie visits Brundlefly for the second time we see Brundlefly walking on the ceiling and wall, however his shirt doesn't remain consistent with gravity. This is especially obvious when he pulls his shirt up to show Ronnie his new tumor and then places it back down. The shirt appears to be being pulled up to towards the sky from Ronnie's perspective. (01:07:30)
Continuity mistake: In the first successful teleportation of the baboon, there is one scene where Brundle's hands move from being straight to folded in just one shot.
Factual error: There is no possible method of "fusing" the genetic material of a common housefly (Musca domestica) and a human. The housefly has twelve chromosomes, humans forty six. There is no way to combine the two in order to produce a viable organism. Thirty four of the human chromosomes would have no matching chromosome to "fuse" with, meaning the physical characteristics coded by those genes would not form. The Brundlefly would be missing three quarters of his human body.
Other mistake: When Seth comes out of the pod for the second time and the girl is watching him she moves her leg reveling panties. However, Seth comes over and they start intercourse. How? He doesn't even move her underwear to one side.
Continuity mistake: When Geena Davis gets kidnapped by the Brundlefly from the hospital, he gets into her hospital room by crashing through a plate glass window. When he leaves through said window we see that a portion of the left side has broken in half and is severely cracked. When John Getz's character attempts to stop them he smashes his hand through the same window section that's somehow become immaculately whole again.
Continuity mistake: When we see the first close-up of Stathis' dissolving hand, we see the fly vomit on his sleeve. In the next two shots of his hand, the vomit is gone. Then, when Stathis has fallen on he ground staring at the dissolved mess that was once is hand, the vomit is back on the sleeve.
Continuity mistake: When Seth cuts the steak in two pieces, one half is larger than the other. He then puts the larger half on the white and brown plate to teleport it. After cooking both pieces, he puts that larger half on the white plate. Seth then gives the smaller half on the white and brown plate to Veronica and tells her it's the piece that was teleported. Furthermore, when Seth cuts a very small piece from the larger half to give to Veronica, the next shot shows two remaining pieces on the white plate although only one piece should remain.