Fired. I'm not squeaky clean and the words 'nutter' or 'effing incompetent muppet' often leak out of my mouth but generally when i've put the phone down - and to said nutter or effing incompetent muppet I am professionalism itself because that is my job and me being a tit isn't going to improve the situation. It's not just the disgusting way they spoke about this person, it is also the fact that they clearly didn't listen or take note of when she said what time she would and wouldn't be in - she could be a serial complainer it's true, but you don't deal deal with people like that by losing your own professionalism.
Like them, my job is working with the general public as well as medical professinoals, social services, police blah, blah, blah... communication is pretty much a key element. If you can't get that basic bit right then there's really no need for you to continue on in my opinion. It's simply gross misconduct.