On the surface, it’s a simple customer service issue: Someone has a problem with your product. They let you know about it. You address the issue and find a solution.

But things can get a bit trickier if your customer service rep is also your CEO — and if he or she is attempting remedy the problem in a very public way.

Earlier this week, besieged media mogul Rupert Murdoch, who by all accounts is actually the man behind 140 characters, responded on Twitter to a person in Kentucky who had an all-too-common newspaper complaint:

Murdoch, who joined Twitter in January 2012 and is known for ruffling a few feathers via the medium (calling Scientology a “weird cult” and giving Mitt Romney campaign advice, for example), was quickly praised by Zilow’s CEO and a branding and social media expert:

Murdoch is a rarity among Fortune 500 CEOs. A July 2012 study conducted by DOMO and CEO.com found that only 4% are on Twitter and 7.6% on Facebook (by contrast, 34% of the U.S. population is on Twitter, and 50% is on Facebook). But an IBM survey of 1,709 CEOs found that, while only 16% use social media, the number is expected to grow to 57% in five years. (A pretty comprehensive list of CEOs taking the plunge can be found here.)

For the leaders who do Tweet, what they’re saying (and doing) can be profound.

“The most spectacular example is is Cory Booker, the mayor of Newark, New Jersey,” Rob Cottingham, a social media expert at Social Signal, told me. Booker regularly engages with constituents, and in December 2010 took to Twitter (and the streets) to help residents during a blizzard. And Craig Newmark, the founder of craigslist, has “customer service rep” in his Twitter bio.

But if a CEO doesn’t know what he or she is doing — or just how incredibly public 140 characters can be — they can create a pretty negative media firestorm. Cottingham points to Kenneth Cole’s ill-advised tweet connecting a spring clothing line to the “uproar in #Cairo” as a particularly boneheaded move.

CEOs also need to be aware that there’s a “certain expectation that they’re responsive like that, and it can look really bad if they’re on twitter and aren’t prepared to have that kind of interaction with their customers,” says Kerry Bodine, co-author of Outside In. As former Best Buy CEO Brian J. Dunn told us in 2010: “You can’t just dabble in social media. You can’t use them only when things are good. You have to deal with rain as well as sunshine.”

Keeping these issues in mind, there’s almost no downside to having CEOs converse with customers, according to Anne Morriss. Morriss, the co-author of Uncommon Service, says Murdoch’s tweets (in this case) were a coup for the Wall Street Journal.

“This is a point in time where newspapers are trying to figure out how to be relevant,” she told me. “The fact that there’s this clearly sophisticated consumer in the middle of the country that is so hungry for this service that they’re going through this trouble to communicate about it in this very brave new-world medium that Twitter has become, is great visitiblity for the paper.”

But we also know that some of Murdoch’s other tweets haven’t been quite as helpful as this week’s, both to the customer and to the News Corp. or Dow Jones brand. Half the battle is figuring out how much leeway your CEO should have, and how to manage a customer’s expectations when a problem arises. Cory Booker, because he lives in Newark, can actually go help shovel snow. It seems more unlikely that Murdoch can singlehandedly fix a newspaper distribution glitch in Kentucky.

“When the CEO gets involved, everyone just automatically scrambles,” says Bodine. “The customer is going to get their issue fixed, and that’s a good thing. But then there’s the expectation that the next person who has a problem is going to respond directly to Murdoch, and the next, and the next, and that’s not a susutainable way to run a customer service department.”

Bodine suggests that combining an active CEO on Twitter as a brand ambassador with a smart customer service strategy could harness the best of both worlds. A CEO could respond directly to a customer complaint on Twitter and include the handle of a corporate account. “It accomplishes two things: Hey, I take your problem seriously as a CEO, but there are other paths for getting this done. [Murdoch] can’t be fielding all their customer service calls because he’s got other stuff to do.” (Like managing a company embroiled in a phone-hacking scandal that’s also in the process of splitting in two).

Cottingham agrees: “If Mayor Sam Adams in Portland says a traffic light’s going to be fixed, then it gets fixed. Your company has to be able to track the commitments your CEO makes, and deliver on them.”

You also need to be realistic about capacity. “A CEO’s time is a strategic resource; use it wisely,” advises Cottingham. “Being open and conversational can be a huge asset. Getting mired in Twitter and Facebook threads while your comptroller can’t get your attention isn’t.”

If you can navigate all this, the rewards of a tweeting CEO may outweigh the risks. “I think this is a deadly serious platform that allows you to, in a pretty revolutionary way, have very public conversations with customers and communicate really quickly what your values are,” explains Morriss. And, importantly, she points out that Twitter is a “cheap and easy” way to connect with customers and lead your employees by example.

In this day in age, New York Times columnist David Carr writes, “the modern chief executive lives behind a wall of communications operatives, many of whom ladle out slop meant to obscure rather than reveal.” Twitter, he says, “has the potential to cut past all that clutter.”

For Rupert Murdoch, Edward Barr, and the Wall Street Journal, that was certainly the case, at least for a brief moment. Both Barr and the Journal declined to comment for this story, though the latter did reveal a brief coda: Barr was, in fact, contacted by a real customer service rep. And hopefully his paper arrived on time this morning.