Here's what I've heard about palmolive (or any liquid dish detergent). If you get a snake with mites, you put ONE DROP of the detergent into a tub of water and then put the snake into the water. If you just put a mite-infested snake in plain water, a bubble of air forms around each mite because of water tension. The detergent breaks that tension, so mites going into the water will drown. This may very well help relieve your snake of many of the mites infesting it at that moment and help it to feel better for the time being. HOWEVER, there's no guarantee that all the mites will drown, and this treatment does nothing about any eggs the mites have lain.
So...palmolive = safe, immediate relief from biting mites.
Provent-a-Mite = safe, permanent solution to a mite problem.