It may be that mold just grows more easily where you live. I wouldn't worry about it. Wipe it off if you wish. I wouldn't bother transferring to a new container, because unless you get rid of the mold issue entirely (such as moving to the desert), it will likely grow back. If your container is plastic you could wipe the moldy areas of the container with vinegar (cheap white works), then put a tight fitting lid on it to keep air out. Molds typically need air to grow.
Even if you get mold growing on the feed itself, simply stirring it in (or scraping it off if there is a whole lot of it) will do the trick. It won't solve your mold problem, but it will keep it under control. The mold won't grow IN the feed, only ON it, because it needs air to grow. The acids and probiotics in the FF will take care of the mold.
I'm absolutely no expert, but from what I understand "bad" mold spores (the evil twins of the "good" stuff we're trying to capture and cultivate for the Fermented Feed) exist everywhere and are virtually impossible to exclude, but they need both moisture and a certain kind of relative humidity to flourish. "Bad" mold spores don't do well in an evaporating environment; they grow better in places where humidity is either trapped or increasing. That's why I suggest leaving the FF container as open as possible ... especially if mold above the active fermenting area has been a problem. You want that area to "dry out" so mold doesn't prefer to grow there.