Have a 4 year old Kenmore HE3t front end washer that will fill with a couple of inches of water when it is not being used. It appears to happen if the door is left open. Any ideas what may be going on?

It could be a defective water fill valve or it could also be that all the water is not draining out on the final spin cycle. After the next time you use the machine turn off the water supply both hot and cold and see if it fills. If it does it is probably the water fill valve.