Question: Is it permissible to wash dishes on Shabbat which do not seem to be necessary on Shabbat but might possibly be?
Answer: In the previous Halachot, we have explained the general rule that one may not wash dishes on Shabbat if they are not necessary for the day of Shabbat itself. The source of this law is that one may not prepare for a weekday on Shabbat. The reason for this prohibition is because one may not exert one’s self on Shabbat for something which is not necessary for Shabbat itself.
Regarding the aforementioned question, we have previously quoted the Gemara in Masechet Shabbat which states that one may wash vessels designated for drinking even on Shabbat afternoon, for there is no set time for drinking (as opposed to a meal which is generally not eaten after the third Shabbat meal).
It seems from the Gemara that even if it is uncertain whether or not the vessels used for drinking will be necessary, as long as it is possible that they will need to be used, they may be washed on Shabbat.
Based on this, it will be permissible to wash soiled dishes on Shabbat as long as there is a possibility that they will become necessary again on Shabbat even if this is not a certainty.
Hagaon Mishnah Berura writes that if one knows that one will surely not be using the dishes anymore, they may not be washed even if they are vessels designated for drinking. This is true, for instance, after sunset when it is forbidden to drink that it is certainly prohibited to wash even glasses and the like.
However, if one is not fully certain, Hagaon Harav Yisrael Yaakov Fisher zt”l writes in his Sefer Even Yisrael (Volume 8, Chapter 32) that as long as there is a possibility that the dishes will be used again on Shabbat, for instance, to serve guests who may arrive at one’s home and the like, one may wash them on Shabbat. Maran Rabbeinu Ovadia Yosef zt”l quotes his opinion as Halacha.
Summary: Those who act leniently and wash dishes on Shabbat even if they are not certain that they will be necessary again on Shabbat have on whom to rely. However, washing pots and dishes which will certainly not be used again on Shabbat as well as washing dishes close to sunset on Motza’ei Shabbat is certainly forbidden.