How do I get mold/mildew out of laundry??

Are they the little black dots from your washer drum? They will continue to happen because your old drum has deteriorated because it's the old enameled kind, not stainless. I hope I'm wrong, because then all you can do is wash in a newer machine.

Spray spots with white vinegar and spray in wash and rewash. If you can add a little bleach. Don't dry until you are sure the spots are gone, may need to repeat.

If you run a cycle on the hottest setting with a cup of vinegar, then another one with 1/2 cup of baking soda it might help. If there is surface mold try cleaning it with the vinegar and baking soda.

Depending on the material the clothing is made of you could try rubbing some isopropyl alcohol on the area that has the spots, then wash

I have gotten that out by soaking in oxyclean for a while!! Keep adding warm water to it every now and then and spray with spray n wash and lightly scrub each time you add the warm water. Soak it in the warm water again. Repeat all this until the stains are gone. I have cleaned dark green and black areas from outdoor fabric using this method. That was so bad I kept it soaking for a week. I was able to get it all out!