Mood rings fluctuate based on changes to the body's temperature. So as zombies are mostly dead with very little blood flow - they wouldn't generate much body heat. (They even show this in scenes where zombies are shown blue on heat cams). It would have been funnier and a lot more accurate if Liv's mood ring only came up black - the coldest color on the mood ring scale.
When Liv is leaving a voicemail for Clive, she starts it with "Wassaaaap" a reference to a popular Budweiser commercial. However, Liv is on the brain of a pageant contestant who has been in a coma since Oct 1998 (date shown in video of the pageant). The Budweiser commercial that's referenced didn't air for the first time until Dec 26, 1999, 14 months after the pageant contestant had been in a coma.