Very useful thread for a newcomer like me. I spent some time following this the discussion and found it fascinating that there is a serious lack of scientific knowledge for the general public. As I am also coming from a science background, I can only explain some of the phenomena by the placebo effect.
I currently have installed a dual cylinder ion exchange softener and it does make life a lot better, especially in terms of cleaning. One thing that I want to raise if that while have the softener hooked up to the main water inlet, I have a bypass tap just for drinking water as I have familial hypertension which I need to avoid excess intake of Na+. Even though the Na+ ion left in the soften water should be very low, it is probably best for some people like me to drink less of it. But so far, I am extremely happy with the efficiency of my softener (same brand as fellow JSHarris' one).