My followup question is: I would like to know the exact status of the mug. In answer to the “question” in the website reply which is copied below, the dishwasher is a Kitchen Aid with a stainless steel interior and racks that are plastic or epoxy coated (the “usual” racks, not stainless steel) and the load of milchig dishes that were run in that cycle did not have any cheese or anything milchig of “significant substance” – i.e. the load that was run contained only dishes, coffee mugs, and cutlery that had been used for milchig coffee, yogurt, and mostly pareve food.
The website answer:
Hello,The status of the mug, if it did become milchig or not would depend on the type of dishwasher the you have, and what it was washed with. However even if the mug did get some milchig taste in it, you are not really using the mug for fleishig, rather for when you are “fleishig”. Therefore, you can continue using the mug even for drinking after a fleishig meal.
If there was only a small amount of actual milk, in the dishwasher and the water dishes, etc. were more than 60 times, the leftover milk etc. that was in it. Coupled with the fact that the water was not heated up inside the dishwasher, rather outside it, which would make the water a kli sheini, plus the fact that you most probably used soap while washing the dishes, you don’t have to worry that it became milky.