I have a Maytag Quiet series dishwasher (dont' remember which model but
I bought it last year. I press 1 button and it does all the cleaning
by itself - has built in "dirty water" sensor to know if it needs to
continue washing or not). But its always been a noisy washer. Every
so often it makes a grinding noise that lasts anything from 10 seconds
to the entire wash cycle.

9 months after putting up with the grinding noise, which was getting
progressively worse, I decided to call Maytag, and a technician came
over and said that it was a known issue with my model that had
defective motors, and that they would replace the motor for free (wich
they did). Replacing the motor helped reduce the grinding noise, but
it is still present every now and then, just not as frequently or as
loud.

Please reply if you find out what is causing this noise, as I'm having
it as well, but at this point I'm assuming its an issue with the
dishwasher design itself. When I put in plates I make sure that there
are no hard food objects inside, so at this point I don't think its
food particles (ex: shells, nuts, etc.) causing the grinding noise.