There is a loud vibrating or rattling noise only during the wash cycle, but it runs fine. The sound seems to be getting louder, but still is working properly, or so it seems. Is there something simple that we could inspect that might be causing the problem?

See if the sprayer at the bottom is caught on something.

Good idea. When we took the sprayer off the gasket underneath was cracked, worth a shot to see if that is the source of the sound. I have to see if it is something that the local appliance store has in stock tomorrow.