I use peroxide. I bought a very cute dress from a second-hand store. I arrived home with it to find mildew stains all along the bottom of the dress that I didn't notice when I was at the store purchasing it.
I researched on the internet on how to remove mildew stains and it was recommended to use peroxide since it works like bleach without the damaging and whitening effects that bleach has. The article also recommended to use white vinegar when you're finished using perioxide to stop the fadening process from causing the fabric to lightening up during the stain removal.
Now when my daughter comes home from daycare with dirt and/or food stains, I dump some peroxide right on the stain with a little bit of laundry soap and let it sit (I sometimes rub it in with a brush to make sure the peroxide and laundry soap really gets into the fibers). I will come back to it after a couple of hours and apply more peroxide. You may need to do this a few times depending on the size of the stain and how long it's been there. Then I wash it and I've been happy since.
This even worked on clothes that were washed and dried that had stains that I missed. For those stains that have been washed and dried already, I usually try the peroxide method on a weekend day since I would need to do this process a few times.
Best of luck to you!