In 2002, when Sen. Paul Wellstone died in a plane crash twelve days before the election, the Minnesota Democratic Party (the DFL) nominated Walter Mondale in his place. Norm Coleman narrowly defeated Mondale IOTL, and that is attributed to the anger against the Democrats generated by the overall partisan feeling at Wellstone's funeral.
Let's say the funeral goes well and is apolitical, and the sympathy vote for the Dems is stepped up. I'm certain Mondale would win, considering he only lost by 2.19% in OTL's election.
What would Senator Mondale do in office from 2003 until 2009? I doubt that Mondale would run for re-election, considering the age and the fact that he really only considered himself the party's replacement for Wellstone on the 2002 ballot. But what would he do in those six years? What would be his effect on America and the world?