Section on dishwashers by Rav Rimon
Clearly, washing meat and dairy dishes together in a dishwasher at the same time is forbidden, as a transfer a taste occurs between the different utensils. The question arises only as to whether or not one can wash meat and dairy in the same dishwasher one after the other. Doing so entails two potential problems. First, the walls of the dishwasher perhaps become non-kosher, given that they absorb both meat and dairy taste. They can then, in turn, render the utensils non-kosher via the water. Secondly, the racks in the dishwasher likely become non-kosher, and they come in direct contact with the utensils. Rav Moshe Feinstein writes (Iggerot Moshe, O.C. 1:104):
"Regarding the new appliance for washing dishes, called 'dishwasher,' whether or not one may wash in it meat utensils and dairy utensils one after the other: It is necessary that what is inside it, meaning, that upon which the utensils are placed, is different for meat utensils and for dairy utensils."
So long as one changes the racks, one may use the dishwasher for meat and dairy utensils one after the other.
But how do we solve the problem concerning the walls? Rav Moshe writes (Y.D. 2:28), "It amounts to many more times than sixty, and we therefore cannot forbid it." Meaning, the remnants of food absorbed by the walls are battel; this solves the problem of the walls, but not the issue concerning the racks.
Rav Ovadya Yosef, in his work, "Issur Ve-heter," adds another consideration:
"The detergent infuses a foul taste into the remnants, and they therefore do not render the dishwasher forbidden, as the Shulchan Arukh writes, 'It appears to me that if they placed earth in the water… even though the grease is stuck, it is permissible, because as a result of the earth it gives a foul taste.' And detergent corrupts taste even more so than earth."
Due to the soap in the water, any taste transferred will be a foul taste, which does not render forbidden that with which it comes in contact, and dishwashing detergent is stronger than ordinary soap.
In conclusion, then, one who uses his dishwasher for meat and dairy utensils one after the other has authorities on whom to rely, provided that he changes the racks and empties the filter. Preferably, however, one should use his dishwasher exclusively for either meat or dairy. If on occasion he needs it for the other type of dishes, he may do so after thoroughly cleaning it and with different racks.