Well, what the heck I'll accept the challenge.
1. Jesse Jackson doesn't call New York "Hymietown" in 1984. Mondale still wins the nomination and loses to Reagan, but Jackson is in better shape going into 1984.
2. Iran Contra goes worse for Reagan/Bush than it did OTL. Instead of coming clean about the Weapons Sale to Iran (well, barely) like in OTL, Reagan continues to lie about it into 1987 and is investigated and the truth comes out, showing both Reagan and Bush had knowledge about it. They don't get impeached or anything, but this really hurts Bush going into 1988, enough for Dole to narrowly take the nomination.
3. Jesse Jackson, who came in second place in the Democratic primaries in OTL, defeats Michael Dukakis, winning the nomination. He moves more toward the center in the General election, has good debate performances against a bland and bitter Senator Dole and goes on to win the Presidential election by a hair. Jackson loses in a landslide to Governor Pete Wilson of California in 1992.