Mould and other bacteria cannot grow in vinegar. What you're seeing is, as Minimatronic states, is the "mother"... see here:
Mother of vinegar is a slime composed of a form of cellulose and acetic acid bacteria that develops on fermenting alcoholic liquids, which turns alcohol into acetic acid with the help of oxygen from the air. It is added to wine, cider, or other alcoholic liquids to produce vinegar.
Mother of vinegar can also form in store-bought vinegar if there is some non-fermented sugar and/or alcohol contained in the vinegar. While not appetizing in appearance, mother of vinegar is completely harmless and vinegar does not have to be discarded because of it. It can be filtered out using a coffee filter, or simply left in and ignored. (Source: Wikipedia).
A lot of us take a tablespoon of unfiltered apple cider vinegar for health benefits each day. The unfiltered version leaves the 'mother' in and is reputed to be beneficial. It doesn't affect the quality of the vinegar at all...