I've had a similar problem with mine. I had it stored under the house where no sun hit it, vents open, no cover, occasional mold.
After having to clean it a couple of times, I started moving it to a spot where it wouldn't get rained on, but did get hit with the afternoon sun. No more mold issues!
We've moved, so it now lives in the basement, vents open, no cover and it's not molded since.
I think having it get some sun and heat up goes a long way in keeping the mold out. I also leave the water pan out to promote more air flow.
When I did have to clean it, I'd scrape off the mold and clean it with whatever household cleaner we use on our counters, and then burn a good fire.