By Beth Kowitt
April 25, 2012

FORTUNE — Wal-Mart’s board is about to step into the spotlight — and don’t expect the glare to subside any time soon.

Along with possible legal consequences, the retailer faces reputational risks and potential managerial disruption over allegations that executives shut down an internal bribery investigation into its Mexico operations in the middle of last decade. Facing claims that senior leaders were involved, Wal-Mart’s (WMT) board will need to determine what happened, and who knew what and when.

“This is one of these nightmare situations for the board,” said David Larcker, director of the corporate governance research program at Stanford’s business school. “You have a responsibility to do risk management and pay attention to all these kinds of issues, but the problem is that, as a board member, you’re not out there doing the internal auditing. You have to rely on information provided by managers.”

Wal-Mart said in a statement yesterday that its audit committee launched an internal inquiry six months ago into the bribery and investigation issues reported by the New York Times over the weekend — issues that the Times alleges current CEO Mike Duke and former CEO Lee Scott were aware of. Scott was CEO at the time, and Duke was head of international.

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Beyond the fact that Scott and Duke both sit on Wal-Mart’s board, the story did not report that any of the company’s directors were aware of the situation. This makes it critical that the company’s audit committee, comprised of independent directors, take the lead on the current inquiry. A spokesperson for Wal-Mart declined to offer comment for this story.

In its statement, Wal-Mart said it had strengthened its global Foreign Corrupt Practices Act bribery law compliance processes, creating a new global FCPA compliance officer role that will oversee five compliance directors based in global markets.

Allen Questrom, former CEO of J.C. Penney (JCP) who served on the Wal-Mart board from 2007 to 2010, said he doesn’t recall discussing FCPA risk during his time as a director. “People have on the agenda things that are immediate,” he said. “There are so many things you have to discuss that you don’t discuss things that have never happened to you before.” He added, “Now that it’s on the table, they’ll bend over to correct it.”

Wal-Mart’s board includes a collection of A-listers, such as former Coca-Cola (KO) CEO Douglas Daft, former CEO of PepsiCo (pep) Steven Reinemund, and Accel Partners manager partner Jim Breyer. Marissa Mayer, Google’s (goog) vice president of local and maps, will stand for election as the latest addition to the board on June 1.

The board members’ other directorships include a handful of companies that have recently come under scrutiny — Goldman Sachs (gs), News Corporation (nws), Green Mountain Coffee Roasters (gmcr) — which, ideally, should give the group a decent sense of how they should navigate the turbulence that’s ahead.

Wal-Mart lists 10 of its 15 directors as independent. The five with direct connections to the company are Duke, Scott, and three members of the Walton family — Rob Walton, his brother Jim Walton, and Rob Walton’s son-in-law Gregory Penner, who previously worked for Wal-Mart in Japan. While Wal-Mart does split its CEO and chairman roles, Rob Walton, not an independent director, holds the chairman position.

MORE: Wal-Mart CEO Mike Duke at risk in bribery allegations

Paul Hodgson, senior research associate at corporate governance ratings agency GMI, says that family members as directors can reinforce a company’s performance because their concerns for success are often aligned with those of shareholders. But beyond the Waltons, he added, there’s a high proportion of what he called outside-related directors for a company of Wal-Mart’s size.

“When you truly start looking at what is an independent board, what truly is an outside director, the way you define it is really difficult,” says Larry Fauver, a professor at the University of Tennessee who focuses on governance. He noted that at Wal-Mart at least half the directors have a connection to the company beyond the board.

Wal-Mart’s scale, $447 billion in revenue and No. 1 on the 2011 Fortune 500 list, does make it hard to find a board member candidate who is affiliated with a company that doesn’t do business with the retail giant in some capacity. But the directors’ relationships are worth pointing out — which Wal-Mart does in its proxy.

The company noted that Accel’s Jim Breyer owned directly and indirectly less than 3% of Kosmix, which Wal-Mart acquired in 2011; certain Accel Funds owned more than 15% of Kosmix and received about $35.7 million in the transaction. The proxy stated that Breyer, who serves as presiding director when the independent board members meet, was not involved in Wal-Mart’s identification of Kosmix as an acquisition target and recused himself from all discussions.

MORE: Wal-Mart tries to recover from Mexico allegations

“He is a venture capitalist so it becomes more likely that he has some kind of direct or indirect investment in a wide range of companies that might be acquired by Wal-Mart,” Hodgson of GMI said in an email. “That’s not to say it doesn’t potentially compromise his independence, but it does explain how it might happen.”

Wal-Mart also does business with companies where its board members are officers. Until October 2011, director Michele Burns was CEO of Mercer, which received $3.64 million for consulting services in fiscal 2012. Additionally, Wal-Mart director Arne Sorenson is CEO of Marriott International, which received $19 million from Wal-Mart for “hotel, lodging, and related services.” Marriott paid Wal-Mart $1 million for purchases.

“If you are fully independent,” says Hodgson, “it’s much easier for you to raise questions than if $19 million of business is riding on your staying in Wal-Mart’s good books.”

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