Nothing wrong with mold spores. Mold is the visible part of the fungi that are responsible for compost degradation. You got moldy vines because the conditions were right, not because there were mold spores in the ground. There are always mold spores in the ground.

So I don't have to worry about what I plant next being moldy?

If what you plant next stays wet and warm, the air-blown mold spores from all over your neighborhood will make it moldy. Doesn't matter much what is in your soil. If what you had was powdery mildew, killing it in your soil won't stop it.

You could put down transparent plastic and solarize your soil over a few weeks, but again, that won't stop the airborne mold spores. Just about the only recourse in mildew infections of plants is to treat it on the plants.

"Moldy" doesn't really help much in terms of description. There are various fungi that could have been on your peas. The first that comes to my mind is that they were covered in powdery mildew.

http://ipm.ucanr.edu/PMG/PESTNOTES/pn7406.html

There are various strains of PM and most are host specific. Meaning they don't jump between different plant families. If this is what your peas had then there is nothing for you to do and whatever you plant next should be fine as long as there is adequate air circulation.

Rodney

Garden peas mildewing when summer gets going is usual, when it turns hot their season is often over. August sowing for a main cropping in October has been suggested in the past, maybe this method has some potential for you. Perhaps your local USDA Cooperative Extension Service branch office has more information, including if August sowing of peas is feasible in your climate. They will certainly know about mildewing of garden pea plants, have something to say about how one might respond to that.

To combine Rodney, and dan's comments, once you figure out if it's host-specific, you then see if there's a way to improve conditions so to lessen the incidence. Oftentimes, as dan points out, it's simply weather and climate related and there's no easy fix. You do what you can to find ways of coping with the problem.

Mold/fungi usually prefer to germinate and grow in cool, dark, stagnate, moist environments. If this is the case, then you can try spacing plants further apart to lessen shade, and increase air flow and drier conditions. Sunlight is another thing you may, or may not have control over. Fungi, for the most part, do not like direct sun. The more direct sun, the less mold.

You can also see if your soil is draining, and the surface is drying out as well as it could. But remember, don't go overboard in think you HAVE to do anything... sometimes the weather is just offering the perfect conditions that season. You might not have the problem for another 10 years. You just learn what conditions favor what growth and act accordingly.

There are remedial actions you can take, and you can learn about those, but growth conditions and diagnoses are the first place to begin.

ETA: was typing as Embothrium was posting...