Yes посуда is a singular noun in Russian, so посуду is its accusative. There is a category of words that are always singular in Russian . For example, картофель (potatoes), марковь (carrots), одежда (clothes). There is also a category words that work the other way: always plural in Russian - деньги (money), часы (watch/clock), шахматы (chess)
This sounds as if посуда equates to "the crockery": an English collective noun that refers to the chinaware that is put on the table for a meal. However, "crockery" only covers plates, bowls and other serving utensils. It does not refer to the dishes, pans etc. in which the meal was cooked. How broad is the category посуда? Does it refer to dishes that you eat from, or those that you cook in, or both?
So with the perfective here, does this sentence mean that 1) we have started washing the dishes at some point, and now we need to finish washing them, or 2) we haven't started washing them, but we need to stop talking at the dinner table and get up and do the dishes this one time, or 3) Neither of these two meanings :P
I hope this question makes sense!