I had moldy closet problems in a couple of my apartments when I couldn't afford much better. I found leaving the closest door open and leaving a fan blowing into the closet helped. I also used diluted bleach on anything that had mold and wouldn't be harmed by such treatment. The bleach killed the mold and helped delay recurrence. If you can - wash your shoes... with bleach if possible. Otherwise, I'd suggest wiping them down with a mild bleach/water mix - testing first on an area that doesn't show to be sure the bleach doesn't have an unwanted affect.
As for keeping the moisture in check, I don't think baking soda would to absorb enough moisture to help for long. I know there's a product used in basements and other typically moist areas that is good for absorbing moisture. I think it's called something like Dri-Z-Air. From what I could tell, you place this in a container that holds the crystal-like product but isn't closed (else the moisture couldn't get to the crystals). It's supposed to help pull the moisture out of the air - kind of like a de-humidifier but not mechanical.
