Wall Street's marquee investment bank is having a hard time finding an untainted board director.

By Beth Kowitt, writer

Lee Scott

FORTUNE – In times like these, companies might need a scorecard to keep track of the alleged misdeeds and missteps of those at the top. Take, for example, an especially problematic seat on the Goldman Sachs (GS) board. On March 19, 2010, Goldman put out a press release announcing the nomination of a new board member -- former Wal-Mart CEO Lee Scott. Goldman was still feeling the heat in the aftermath of the financial crisis, and Scott had the right résumé and experience. After all, he had led Wal-Mart through its own public relations troubles.

Two months later Goldman CEO Lloyd Blankfein announced that he was launching a business standards committee; Scott would be one of four board members on it. But Scott stayed on the board for just a year. When he left, in 2011, he said it was because of time constraints.

Then, in late April of this year, the New York Times reported claims of bribery by Wal-Mart (WMT) officials in Mexico, along with a problematic internal investigation into the bribes. The paper alleged that Scott, then Wal-Mart CEO, had known about the investigation. (Scott was CEO from 2000 to 2009.) Though the trouble in Mexico occurred before Scott joined the Goldman board and he had left by the time allegations were made public, Scott's short directorship could undermine the time he spent at Goldman. After all, he was on the company's business standards committee. Even worse, he joined the board just as a notorious member was on his way out.

Rajat Gupta

The same day that Goldman announced Scott's nomination -- March 19, 2010 -- it filed an 8-K stating that current board member Rajat Gupta would not stand for reelection. A month later news broke that Gupta was being investigated for allegedly passing along inside information gleaned from his position as a director at the company. Both Goldman and Scott declined to comment.

Heavy-hitters like Gupta and Scott bring visibility to a company's board -- generally a desirable attribute, until it isn't. "You don't want those things cropping up and have people start second-guessing what you're doing," says David Larcker, director of the corporate governance research program at Stanford Graduate School of Business. Maybe a scorecard really is in order.

Gupta's online support

Rajat Gupta began his trial for securities fraud armed with the same secret weapon deployed by Martha Stewart and Raj Rajaratnam: a website with messages from the defendant's supporters. A sampler from friendsofrajat.com:

"He always quoted the Bhagavad Gita ... 'You are only entitled to do your duty, not to the fruits of that duty,' and he lived by that credo." --Mukesh Ambani, chairman, Reliance Industries Limited

"I first got to know of Rajat as a distant iconic inspiration, not merely to me, but to the entire Indian community in the U.S." --Rohini Dey, founder, Vermilion restaurant

"I have seen him ... help everyone who reaches out to him ... He personally reached out to his colleague to put us in touch for a business deal." --Sabeer Bhatia, co-founder, Hotmail

"As a person, he was very affectionate and considerate." --Sujatha Rao, former Secretary of the Ministry of Health, India

This story is from the June 11, 2012 issue of Fortune.