I googled felting yesterday to get tips for my own project and I'm pretty sure one website said NOT to use dish soap. It said that's the worst thing to use when you want to felt something. I think it had something to do with the dish soap preventing the fibers from sticking to each other. Here is the article: http://www.fuzzygalore.biz/articles/fulling.shtml
Here is what it says: We use Dawn dishwashing liquid to wash our sweaters because it's what preserves their condition best, cleaning without stripping, preventing dye bleeds, and not disturbing the scales so there's less chance of fulling. So consequently it's the worst possible thing to use when you mean to full. There is still some liquid soap available on the market, like some varieties of Ivory, or you can use Ivory soap flakes, or even a plain bar of soap.
Fulling and felting are essentially the same thing, right?