How did the legacies of Watergate and the Vietnam War shape US politics?

Prior to Watergate and Vietnam, the American people had great faith in the American Presidency. Men like FDR and John F. Kennedy were trusted leaders. The Pentagon Papers exposed a failed Vietnam strategy and the inflation of monthly body count numbers by the Lyndon Johnson administration. Watergate exposed Richard Nixon as an obstructionist of justice and the secret bombing of Laos and invasion of Cambodia went against his Vietnamization policy. The secret dealings of these Presidents and our government caused distrust among the American people and fueled the antiwar movement. The American presidency would never be the same, as leaders would be forever scrutinized rather than blindly trusted. Respect of the President would not automatically come with the office.

The Vietnam War and Watergate were polarizing events that took place during a very volatile period of US history.
While during most of the twentieth century, Americans had been able to pull together despite deep ideological and political differences to tackle crises such as the Great Depression and World War II, this political consensus or center fell apart during the Vietnam War and Watergate period.
People didn't coalesce around the Vietnam war, for instance, as they had about World War II, which had extremely high support. Instead, the country split. Some supported the war as necessary to stop communism while some saw it as a mismanaged mistake and felt we had no reason to be so heavily involved in a tiny country halfway around the globe. As the debate over the war continued, there was no common ground. Emotions ran high and each side demonized the other.
This continued into the Watergate hearings. Those who opposed the war felt Nixon was a criminal who needed to be held accountable for continual lying and law breaking. To them, authorizing the break-in of the Democratic National committee headquarters at the Watergate hotel was of a piece with such acts as the secret bombing of Cambodia. This side of America felt Nixon should be punished. Those who supported Nixon thought the impeachment hearings were a witch hunt.
After things settled down, resentments lingering. They linger to this day. The worst legacy in terms of politics is the polarization. Government has been paralyzed, especially in recent years, because the two sides demonize each other. It is hard to work with people you disagree with if you think of them as evil incarnate. Arguably everyone still suffers because the wounds of fifty years ago have never properly healed.