True, particularly with yeasts from secondary. I plan to buy a stir plate, then when I buy a vial of liquid yeasts I could make a step-up starter with fresh yeast and have enough yeast for a couple of brews.Something to bear in mind, don't recycle your yeast too many times.
Good you have identified the source of infection. I plan on moving from oxi sanitizer to StarSan. I am also thinking about replacing my washing up liquid with something else. I read in Palmer's book not to use scented liquids and that generally washing up liquids kill the beer head. I use a non-scented washing up liquid, but maybe I will try PBW?
As you say, there is always something to learn