http://www.cinemablend.com/new/Stallone-You-Guide-Bruce-Willis-Other-Famous-Feuds-38890.html

Moonlighting
The 80s sitcom that launched Willis to fame well before he walked on broken glass as John McClane, Moonlighting paired him up with Cybill Shepherd as a pair of detectives who squabble but, of course, give in to some sexual tension as well. As Willis's career took off his relationship with Shepherd and even some of the crew worsened; here's how the show's producer Jay Daniel explained it in this interview:

Everybody knows there was friction between the two of them on the stage. In the beginning, Bruce was just a guy’s guy. Let's just say he evolved. Over the years, he went from being the crew's best friend and just being grateful for the work and all of that to realizing that he was going to be a movie star and wanting to move on. Part of that was because of his strained relationship with Cybill. That sometimes made the set a very unpleasant place to be.

Curtis Armstrong talked about Moonlighting extensively in his book. Basically, Bruce Wills was painted was an arrogant a-hole who thought his crap didn't stink once the show became a hit. Armstrong was brought on because Bruce started to resent all the slapstick he was given, and wanted more serious storylines so movie studios would take note of his range and cast him. When he won the Emmy it got worse, and by Die Hard, he had all but checked out of doing the show. The staff simply put, hated him. They weren't fans of Cybill Shepherd either, but unlike Cybill, Glenn had a bromance with Bruce, and thought he could do no wrong. So he got a pass for his wretched behavior, which included belittling people on set in front of everyone if he was in a bad mood.