Second on the sunlight, it's excellent for killing mildew, especially on natural fibers.
To get rid of the residual visible stains, you might want to look into one of the spray-on carpet or upholstery cleaners you can find in an auto-parts store. Not the most eco-friendly stuff, but presumably you are not going into a high-volume guitar case cleaning business.
Make sure to test on an inconspicuous place, as it will no doubt say on the package!
For leather-ish covered cases, which seem to attract mildew with a vengeance, I have had good luck with either a dilute laundry bleach wipe, or a solution of plain trisodium phosphate (laundry detergent without all the fragrance and brighteners, available at hardware stores). But I wouldn't try the bleach on textiles.
-Glenn