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 1986 the only Space Camp was in Huntsville, Alabama. There's no way Kevin and Kathrine drove from Alabama to Florida to see the shuttle on the pad. They couldn't have made the drive in a single night in Kevin's Jeep and be back to Space Camp in the same night.
Plot hole: Near the end of the movie, when Packard is about to race the Turbo, he puts on a helmet. Where exactly did he keep this helmet? The '77 Corvette is a two-seater with very little storage space for the passengers. Oggie and Minty's helmets could have been in the back seats of their cars.
Plot hole: If the Bird-of-Prey went to warp speed right after the whales were beamed up the ship would have already been so far away from Earth it would have been on its way back towards the sun, yet minutes later the ship is shown leaving the Earth, still at warp speed.
Suggested correction: Being as how the bacteria and mites and such were IN or ON Seth, the machine was able to organize those symbiotic relationships accordingly as teleporting one would teleport all. The fly was separate, not touching. The machine was not programmed to anticipate two separated entities and so combined them into one on the other side.
Phixius ★
We leave behind a vapour trail of bacteria and viruses (among other things) as we walk, in our breath and emanations from pores in our skin, and Brundle isn't trapping any in his clothes as he isn't wearing any. Brundle has an invisible cloud of DNA floating around him in that teleportation chamber and as far as the machine is concerned their DNA has exactly the same status as that of the fly.
We don't know enough about how the machine works to determine how it might differentiate different DNA types. Unexplained science means it's somehow able to do it. Willing suspension of disbelief for the win.