"You have never even washed a plate."
Translation:Nikdy jsi neumyl ani talíř.
It is a grammatically correct sentence, but it is strange. Normally when you start to wash a plate, you wash it completely. At least in this kind of question. Nikdy jsi nemyl... is like You were never washing... It just does not make a good sense to me for a plate.
Nikdy si nemyl nádobí. is better, that one is not something definite like a plate, but it is about washing up dishes in general. It implies the repeated action, every time someone was washing up, it wasn't you who was doing it.