Now for a reason why you shouldn't use it to respond to customer complaints: The second word gets out that using Twitter gets you better customer service, everyone will use Twitter. And unlike the occasional good PR that comes with Twitter, you now have a reputation for not doing things right in the first place. Availability bias is a bitch.
Nitpicking but... I'd say responding to complaints on Twitter is a great idea, but just to show you're listening and then as an arrow pointing to the correct channel for resolving an issue
