One of the major factors behind the rise of big data is the whole social media analysis thing. It helps you to decide what best offer you can make to customers or to understand how and why they are disgruntled and what you can do about it. And, in particular, it allows you to do this very precisely, down to the level of the individual customer.
However, there is a big problem hiding behind this thought: it presupposes that you know who your customers are in the first place. You need to know if this particular customer makes you money, and if so how much, or if they actually cost you money. There is no point in making them an offer (except perhaps to go away) if they aren't profitable customers in the first place.
So, what does that mean? Well, it means that you need to have the whole paraphernalia of data governance (to ensure that your understanding of customers is valid and correct) and analytics (such as customer profitability analyses) in place before it is worth jumping on this particular big data bandwagon. And, of course, the same thing would apply if you are using big data analyses to enhance your understanding of products or suppliers or anything else within the corporate ecosphere - if you don't have a proper understanding of whatever it is you are analysing in the first place then adding more data to an already confused picture will only make it more confusing.
I haven't yet heard about any big data disaster stories but no doubt they will come. And I expect they will come from companies that have bought into the whole big data thing as a panacea and haven't focused enough on the small data that they already have.