I have actually thought about this, since this is a chore that I absolutely hate. In my view no one should be subject to the task of making dishes. Some people seem to like it, God bless them !
Initial prototype will be to work with steel utensils to avoid damages. Current object detection techniques are sufficient to recognize plates, glasses, dirt etc.
I envision a setup something like this - two robotic hands sitting on top of the wash basin with a camera head. One of the hands has a built in tap and the other a detachable scrubber with soap dispenser. One arm picks up the utensil, rotates as required, sprays water as required. The other arm scrubs off the dirt until it's clean.A camera module watches until the cleaning is accomplished. Once clean, first arm piles up similar dishes in stacks.
This made up for a good hallway conversation and I had forgotten about it since then. Thanks for rekindling the thought.