When you say not lacking in vinegar, how much are we talking? It should be a minimum of 1/10th 5% acetic acid vinegar by volume to get you to a pH around 3.5-4.0. Lower acidity vinegar and you'll need more. Higher pH starting sauce and you'll need more vinegar. It's something that I don't gamble with and $50 for a good quality pH meter means you are sure to be safe.
And an unused woozy has no guarantee to be sterile - you have no idea where it's come from and what was done to it before you got it. I have received "new" bottles that didn't look all that clean. Always wash and sterilize new bottles before using.
Finally, are you sure it's mold? What does your nose tell you? It could just be the sauce separating. It's funny that it's in the middle of the bottle as mold usually grows on the top.