Customers tweeting complaints @yourcompany are easily overheard, but what about those tweeting about you, rather than @you?
Take this customer's experience with John Lewis: when phone channels failed to solve their problem they tweeted about their frustration, and @ JLcustserv jumped in. Going out of your way to track down customers in need of assistance is excellent social customer service.
Why not tweet @you?
Twitter can be used for personal conversations, but is also a platform for expressing feelings, often frustration. Someone annoyed with your company might not always be looking to engage with your customer service agents, and won't bother to find your account.
Your angry customer might be looking to speak to you on Twitter but can't find your handle, either because of your obscure name or confusingly copious accounts, (this is common in large companies: Dell for example has over 15 different accounts).
Why bother?
It's obvious why you want to catch tweets from those who haven't quite managed to find you on Twitter, but why would you want to talk to a customer who isn't talking @you on purpose?
Those posts bemoaning a bad experience with your company are aimed at spreading a negative impression of your brand. Offer them a more positive experience of your customer service on twitter and not only can you win back your unhappy customer, but they will often broadcast the unexpectedly positive experience to their followers.
Twitter PR disasters can flare up from any mention of your business, regardless of whether they @mention you or not. Twitter users won't discriminate in the same way as you if you're missing them, so keeping track of every conversation matters.
What to do?
Keep an eye on all conversations about your brand, not just those which conveniently show up on your Twitter feed. For Conversocial users it's easy to keep up using custom saved searches, which can present you with anything you like: your company name, major products, or any variations. These can be managed and assigned to team members in the same way as @mentions.
Take care of those calling out in frustration, and you might just turn them into your biggest fans.