They say that there is a word for a phobia for everything, but googling the fear of dirty dishes or fear of doing the dishes results in a void of a term.
The adjective dirty in Greek is μυσαρός (mysapos), while a dish, pot or pan is λέκος (lecos) (ref. LSJ).
Mysophobia is the fear of dirt and μύσος is a noun, which has been used as an adjective only in Hesychius' dictionary of obscure words.
Regarding the word for dish, there are many words to choose from: earthernware, Lydian etc., but I think lecos is the most vague and quite common so fits the bill.
So the word for the fear of dirty dishes is mysapolecophobia!
The word for "fear of having to do the dishes" is a quite a bit more complicated. To do the dishes is hard to translate as the verb to do is often a magical verb that fills a hole. Washing-up does not given anything in Perseus, so the trick of using modern Greek, which has a richer presence on the internet gives "πλένω τα πιάτα", πιάτα being an obvious import (cf. Italian piatto and English plate) and πλένω being to wash in modern. The Attic equivalent being πλύνω. When someone says Greek is easy, they are a clueless braggart or a genius as Greek verbs (v. http://en.wikipedia.org/wiki/Ancient_Greek_verbs) are a product of a culture that spent too much time walking under the heat of the sun naked while talking about the meaning of the universe. Skipping the grammar discussion, I get the verbal adjective πλυτέος (masculine) or πλυτέον (neuter). So the fear of having to do the dishes is plyteolecophobia (literally, the fear of the dishes needing a wash).
So if one just fears washing the dishes which are dirty, one could be said to be plyteomysapolecophobic. That word is a tad hippopotomonstrosesquippedalian...
