Dish soap is predominantly comprised of "detergent" (and sometimes phosphates), along with a relatively small amount of anionic surfactant to improve the wetting of soiled dishware.
1) It takes a relatively large quantity of dish soap to equal the surfactant-load found in a quality (concentrated) adjuvant that is designed for herbicide-use.
2) Commercial adjuvants are normally non-ionic, versus anionic dish soap. Virtually all herbicides specify the use of non-ionic surfactants for optimum performance.
3) Higher use-rates of dish soap (to offset its lower concentration of surfactant) will guarantee that the second tank-load will "foam-over" (foam exiting through the tank-lid) long before the tank is half-full - unless one uses a additional defoaming agent (PAM sometimes works).
4) Surfactants play a much more important role than simply wetting the leaf-surface; which is comprised of multiple layers of overlapping/waxy platelets (ie. leaf-cuticle). Systemic herbicide spray-depositions must permeate the leaf-cuticle without causing tissue-damage in order for the herbicide to enter the plant's vascular system. With systemic herbicides, damage to the leaf-cuticle may prompt "shock" (shutdown) in the treated plant's metabolism - and impede the herbicide's mode-of-action, which often involves enzyme synthesis disrutpion. In other words, treated leaves may turn brown - but the herbicide was unable to perform its mission, and such plants often survive in the long-run. Same thing happens when one uses too much herbicide (an excessive concentration). Short-term results from the shock-effect may look good, but a quick visual response is often deceiving.

I'll stop boring you with details (finally) and give you my opinion.

Dish soap is probably better than nothing; but is far inferior to a quality commercial surfactant when a herbicide label calls for it.

Kelly Duffie
Cypress, TX