Like a previous post mentioned, I would actually take it a bit farther and suggest that Vietnam has taught us very little. Many Americans think that the wars in Iraq or Afghanistan were improper or even illegal, particularly after some of the propaganda was burned through, but do we see huge numbers of young people protesting?
I would argue that one of the lessons learned was that having a draft for an unpopular war is very likely to get it ended because of political pressure so politicians have made sure to find ways to conduct their wars without having to institute a draft. Instead we use huge numbers of mercenaries with their inherent problems because it allows those in power to pursue their agenda without the political pressure that might be brought to bear if everyone had children and friends being drafted.
I think one can say that Vietnam has caused lasting change in that it is constantly used as a reminder whenever the United States enters into a military conflict with a foreign nation. Terms like "like Vietnam" or a "Vietnam like situation" or "another Vietnam" are immediate flags for any sitting politician and something that is completely in the "hearts and minds" of those who are in the position of power. I think that the military treatment of the media has also been impacted since Vietnam. The idea of an "embedded journalist" with troops that "can report" certain elements is a direct result of the media angle to Vietnam, a component that caused great challenge to the authority structure. In line with this would be the ban on showing military caskets, a throwback to the Vietnam War when the media was able to show the deaths of military servicemen with open and uncensored access. The looming specter of fighting a war abroad without clearly defined aims or precisely articulated and adhered goals becomes a realm where the Vietnam War has altered the policies and practices of the United States.
I think you can argue that the experience in Vietnam made the US think harder about being less assertive in its foreign policy. I think that this experience made the US feel that military force was not always the right way to advance US interests around the globe.
The Vietnam experience showed American leaders that overwhelming military force could not cause the people of another country to like America and agree with our ideals. This made them much more cautious about using military force in cases where we needed to win over the people of a country (rather than just defeating them militarily).
I would say that Vietnam did cause lasting change in the sense that it really affected our response to things like the Iraqi invasion of Kuwait and the situation in Somalia. However, you can argue that our involvement in Afghanistan shows that we have not completely learned the lesson of Vietnam.