The main impact of the Vietnam War was to help drive American society apart. American society had been relatively homogeneous and united in the 1950s and early 1960s. The war helped to break this homogeneity and bring on the "culture wars" that we now have.
The Vietnam War helped to split American attitudes towards things like patriotism and authority. The traditionalists wanted to keep hold of ideas like respect for authority and support for US foreign policy. People who were radicalized by the war, on the other hand, started to feel that patriotism and authority in general was corrupt and should be resisted.
The Vietnam War helped to force this change in American attitudes, creating a split that had not previously existed.
The Vietnam War was a watershed moment in American history. After Vietnam, Americans did not trust their government as much. Press briefings from the Oval Office said that America was winning the Vietnam War, but the Tet Offensive in 1968 demonstrated that the Vietcong and North Vietnamese Army were still viable forces. People did not put all of their faith in experts as well--Robert McNamara, Johnson's Secretary of Defense, used data such as kill counts and bomb tonnage in describing the war, yet the daily televised coverage of the war told a different story from that told by the administration. Young people became more active in politics and demonstrating against the war. Their active involvement in protesting the war led to the 26th Amendment, which gave eighteen-year-olds the right to vote. More young men went to college to seek draft deferments, but the increased college enrollment can also be attributed to factories closing all over America. Also, more Americans experimented with drugs during this era and there are still questions in American society about the legalization of certain drugs.
The Vietnam War also split society in terms of people's view of government. Nixon won the White House in 1968 and 1972 by calling on the "Silent Majority" who still supported their government with few questions. Soldiers and draft protesters regarded each other with animosity for years after the war was over. The Vietnam War made Americans seriously question whether or not it was proper to criticize the government and what methods should be used to protest.