Data mining and intercepting bad company experiences and "making good" on them. For example, we had something delivered via UPS. The driver left it on our front step, didn't ring the doorbell, and just left. It sat out there for hours before we realized it was there. The package could have easily been stolen during that time and neither UPS nor I would have known until it was much too late. We complained on Twitter and UPS contacted us in an attempt to find out what went wrong and how they could improve their policies.
I think this is a bit of a red herring. If the company cares about customer service then you shouldn't need to complain on a public forum to get them to pay attention - they should provide a customer support line and actually take all calls to it seriously.
Spot bad experiences, help minimize bad PR by helping those customers, and minimize future bad PR by fixing those problems before more customers are affected.
Now you've hit the nail on the head. Social media is actually a problem for companies: prior to social media, a company screws up, you complain, they ignore you, you moan about it to about 3 of your mates. Now, a company screws up, you complain, they ignore you, you moan about it on twitter, it goes viral and a hundred thousand people see how badly the company treated you. The company isn't interested in helping their customer (if they were, they would've helped their customer whether or not it turned into a PR disaster), instead they are interested in avoiding really bad PR - really bad PR that wouldn't ever have happened without social media.
I don't use Twitter, but I have sometimes wondered whether its worth getting an account just to make complaints, since complaints on Twitter seem to attract a much quicker and more helpful response than calls directly to customer services.