The slime infestation was all Rankin's fault
If you'll remember, the slime got onto Gamma 3 because of a tear in Dr. Halvorsen's suit which a slime fragment had gotten into. It looks like the tear was caused when Rankin snatched the containment unit out of the doctor's hands and smashed it against the ground right in front of them. I know they were pressed for time, so he couldn't stop to argue over quarantine rules and the like, but Rankin should've tossed it into the distance... for all he knew, the thing could've reacted to high impact by exploding!
Frankly, Rankin strikes me as a guy trying to be Captain Kirk a bit too hard, and it was this first unnecessary macho action of the movie that was the catalyst for the rest. Not that Elliot's soft-heartedness didn't cause some bad decisions, but Rankin's hard-_headedness_ started matters to begin with.