Hi, Richard! You'll always want your starter to be loosely covered, since your yeast needs air to breathe. Leaving it in the same container is just fine, although some people prefer to move theirs to a new container; it's just a matter of preference. If you've repeatedly gotten mold or other things growing on your starter, it may be that there's something growing in a hidden place in your kitchen (inside walls or under appliances are common places) that's shedding spores. Sometimes just keeping your starter in another part of the house is enough of a change to keep your starter from getting the funk. Best of luck, and happy baking! 

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