Whatever you do, don't use bleach... The whitening only works temporarily, and in the mean time it breaks down the vinyl making it more susceptible to staining in the future. It also tends to break down the thread in the seams causing it to fail prematurely too.
Specifically for spot cleaning the mildew stains, you might want to try lemon juice, a pinch of baking soda, and a toothbrush. Scrub it in with the toothbrush and then let it sit wet on the stain for 30 to 60 minutes. Afterwards, give it a final scrub and wipe it away.