Wash several loads of clothes without any additives, soap, Downy, anything. If your clothes are still getting the greasy looking spots on them call a reapirman or buy a new washer. This happened to me several years ago, my husband "helped out" by doing a couple of loads of laundry and they had greasy spots on them. I didn't use Downy at the time so I accused him of ruining my clothes. Eventually we found the washer had broken beyond repair. The grease from the motor was floating up and my washer was so old that it was just cost effective to purchase new.
I use Downy in just about every load now and I do not have a problem with spots. Ever.