As a kid I grew up on a farm, that was over thirty years ago, so things have changed, but we used a cleaner to get off milk residue that would build up on the stainless. There would be this blue hue on the stainless that was hard to scrub off, but the cleaner we used would take it right off. It would also dry out your hands. We still had to use Clorox for final sanitation.
I may have to look into this stuff that Velward mentions if I have problems. In New York State, however, you still have to use diluted chlorine as a final sanitizer. It's the only thing they will accept. I'm not sure if there is scientific basis for that or that government regulations are slow to change.