The quality turns to shit mostly in shots where it looks like they lost light during filming (Mac talking about having set up the tripwires is the worst), which is understandable if the film stock they were using wasn't rated for the lighting conditions and they had to push it in the lab.
At the end with Arnie and the Pred's cat and mouse game, where the entire sequence is at night, the quality is largely consistent, which you'd expect if they were filming with an appropriate film stock.
(Alternatively the low-light stock they had on location was shit, which would equally explain it. Either way, stock problems.)