The idea of President Bill Clinton as a tragic hero is an interesting one. Usually a tragic hero is defined as someone whose general nature is noble, but whose tragic flaw brings about their downfall. Tragic heroes are also usually of noble birth; this was not true of Clinton, but his humble upbringing with a single parent and his determination to be successful led to exceptional performance in academia (he became a Rhodes Scholar), and made him a very admired politician.
In Clinton's case, the most significant event of his presidency was the attempt to impeach him following the discovery that he'd had an extramarital affair with an intern, Monica Lewinsky. Impeachment is a dramatic event and happens rarely to sitting presidents; when an attempt was made to impeach Richard Nixon over crimes committed during the Watergate event, he resigned first. Clinton stayed the course, perhaps knowing that public opinion would help support him in the midst of an inappropriate persecution by the Republican Congress, and in the end he was not impeached.
The issues around the hearing and investigation were contextualized by saying that Clinton's lying under oath about the affair somehow constituted impeachable offenses. Some Americans thought he was unfit for office because of his actions; but many more people believed his personal life was not relevant to his work as President, and resented the time and expense of the investigation. It is also generally well known that many politicians and powerful people engage in affairs and it does not appear to affect their efficacy in their jobs (at the time it was mentioned in media that President Kennedy was suspected of a number of extramarital affairs). As well, the notion that Clinton should be impeached for behavior common in politics seemed to many to be hypocritical.
This is where one can begin to identify the tragic flaw associated with this kind of behavior. In Mr. Clinton's case, his tragic flaw could be any number of personality traits associated with his actions, but I think a good one that stands out is charisma. Clinton's personal charisma not only helped move him forward in politics, but makes him attractive to women. Just as politicians are said to engage in various kinds of corrupt behavior because they feel powerful, Clinton's charismatic personality was fed by admiration and the political power associated with being a Senator, Governor and President. That charisma helped him feel invincible and impervious to judgment.