I think there may be a danger in labeling yourself based on your weaknesses. It could lead to subconsciously shutting down options because they involve your "weakness". Essentially, if you don't explore your weakness and try to gain strength in that area then you risk letting it atrophy.

For example, if you're a "technically-savvy, introverted programmer" and you hire in a "outgoing marketeer" to handle all the customer relations then you may find that you loose touch with customers and loose sight of the company as a whole.