Question: Can I clear off the dirty dishes from my table and load them into the dishwasher on Shabbos?
Answer: Chazal (Shabbos 114b; 118a) decreed that one mustn’t prepare on Shabbos or Yom Tov for the following day (See Shulchan Aruch OC 302:3; 503:1). Different reasons are offered for this prohibition. According to Rashi (Shabbos 114b) the extra tircha, effort, that one has to expend is inappropriate on Shabbos (See Mishna Berura 323:28). Rambam (Shabbos 23:7), however, writes that hachana, preparation, is akin to mesaken¸ fixing something.
The Mishna Berura (503:1) explains that this applies even to an action that isn’t a forbidden melacha, such as washing dishes. Thus, the Shulchan Aruch (OC 323:6) writes that it is forbidden to wash dishes on Shabbos for use after Shabbos.
The Mishna Berura (302:19) writes, however, that while one can’t make one’s bed on Shabbos for the following day, if one is bothered by it being unmade, then one can make it on Shabbos as that is considered to be a Shabbos necessity. Thus, R’ Yehoshua Neuwirth (Shemiras Shabbos Kehilchasa 12:35) writes that if one typically clears the table during the week and places the dirty dishes straight into the dishwasher, they may do so on Shabbos, too.
Likewise, R’ Moshe Feinstein (Igros Moshe OC 4:74, rechitza 4) writes that as people don’t like seeing dirty dishes left out, there is no issue with putting them into the dishwasher. One mustn’t sort the dishes as that would be an issue of borer, though one can take all the large plates off together and put those in together, etc. (See Baer Moshe 3:48).
In conclusion, one may put one’s dirty dishes into a dishwasher on Shabbos though they should be careful not to sort them.