Hated when Sigourney... (spoilers)
When she died. I know it was done to exacerbate Murphy's character's motivation, but it was still very depressing and basically unnecessary. The movie goes downhill from there. Their interaction was pretty much the most interesting part of the movie (next to debunking).
Reminds me of the moment when Sup's dad dies and Sup's pissed because he can't stop a heart attack. But that was more effective than this.