The Fighting Between Bruce and Cybill
I always thought it was her fault because of other accounts with her not getting along with co-stars, but I'm not so sure if that was the case. I doubt that they hate eachother, and they may even have a friendship of some sort, but I remember always reading about the infighting while the show was on. She resented him becoming a bigger star than she was. She even commented when he was on the rise that he was just a bar tender a few years ago, as if she didn't feel like he had paid his dues enough to pass her up like he had.
Anyway, I'm watching this http://www.youtube.com/watch?v=R69XVxZ6ZEo and while they seem friendly, you can feel an odd tension every now and again, and right before the segment ends (starting at 9:15) Bruce gets in a dig at Cybill, thanking her for getting pregnant, which allowed him to do the first Die Hard, and he said "we all know how that turned out".
Was that really necessary? You could tell she knew it was a dig at her, but she remained professional on the camera.