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.
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.
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.
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?
Visible crew/equipment: When Jeff Goldblum is first showing his telepods to Geena Davis, as the door to the first pod opens, you can see a reflection of a stage hand in the lower left corner of the pod door.
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.
Character mistake: Brundle's steak experiment has one major flaw in its planning: he takes care to separate the two cuts of meat by placing them on different coloured plates so he knows which is the control cut and which is the teleported cut, however he then proceeds to cook them both at the same time in the same pan. Being a scientist you'd think he'd know this could quite easily ruin the results of the experiment as whatever changes occurred to the teleported steak could leak out with its juices and contaminate the control.
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.
Visible crew/equipment: After Seth Brundle has gone through his final stage of metamorphosising into the Brundlefly, he throws Ronnie (Geena Davis) into one telepod and then starts to make his way across the lab towards the other one. Watch as he emerges from behind a wooden pillar, there's one shot where a crew member's arm is seen reaching inside the back of the Brundlefly puppet, to move the creature's head. You'll need to slow-mo to see it but it's there. (As per the rules of this site, visible crew members is an acceptable use of slow motion.)
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 Jeff Goldblum's character tries to fix the flaws in his telepods by transporting a steak through them, we see him place the steak on a white platter before placing it in one of the pods. When the steak gets transported it appears in the other pod on a dark blue coloured platter.