If you put a woodstove in the basement , the wood will dry so fast, it will actually get so dry it will burn up fast. My parents have done this for 30 plus years with a forced hot air wood furnace in the basement. They only throw down a months wood at a time, otherwise it overdrys and burns way too fast.
Bugs.....bugs....bugs. That's a problem with wood in the basement.
Mold, not even a chance if there is a woodstove thats burned regularly in the basement. Without the woodstove, it could happen, but probably not if you heat it anyway.