There are many ways to approach this particular question. I would say that one particularly harmful action was that the United States was more focused on external threats during the Cold War than fully pursuing a developed domestic campaign on issues that impacted the daily lives of Americans. The Cold War obsession helped to crowd out issues of health care, education, and urban renewal. At the same time, I would say that the destructive element of collectivity, being able to identify ourselves as "Americans" vis a vis the relationship against the Soviet Union and not fully grasp the dynamics of the different groups in America at the time was harmful. A constructive dialogue on race, gender, class conditions, sexual orientation, as well as other valences of identity was deferred while the national discourse was driven by the defeat of the Soviet Union.
One that hasn't yet been mentioned is the enormous amounts of spending based on estimates of Soviet power including both conventional weapons and nuclear weapons. We know now that we overestimated the actual amount of weapons the Soviet Union had on almost every level and we spent huge amounts of money building up weapons that (hopefully) will never be used. The billions of dollars that were spent on projects of enormously limited utility, for example the triangle shaped stealth bomber that would take off from a carrier, were completely wasted. They might very well have used this money for more effective purposes, but one would also argue that we were acting on the intelligence we had at the time so...
A second might be the incredible emphasis on the idea of us and them, two sides that can only be opposed and will never actually be able to reach an agreement. We have a huge problem in this country because every issue is almost always portrayed as right or wrong and black and white. With the Cold War it was either us or them and we were willing to go to places like Korea and Vietnam to fight against the Soviets in proxy.
This lack of openness is never helpful in terms of helping a society to be open minded or to help both its own people grow and advance as well as being willing to do things for the good of the rest of the world.
I'd say there were many more than two. The Second Red Scare and McCarthyism I would agree were harmful in that it turned Americans against one another and made them fear each other. Four continuous years of accusations and hearings created a long lasting hysteria, and demonized the words communist and socialist so much that you still see them tossed around as political criticisms today.
Another harmful event was the Cuban Missile Crisis. The society now realized and believed that the end of the world was possible and near, and they were helpless to do much to stop it. While Kennedy's handling of the crisis made people more confident in his leaderhsip skills, it also hurt some peoples' confidence in government everywhere, that it would lead societies to the brink of annihilation.
I suppose you could say that the McCarthyism of the early 1950s was a US Cold War action that was harmful to American society. By setting up an atmosphere of distrust and intolerance, McCarthy and the other communist hunters, you can argue, made American society much less happy and free.
A second action, I suppose, would be the Vietnam War. This harmed American society by driving such a wedge between people in the US. The people who were for and against the war disliked each other so much that it, I think, helped lead to the kind of cultural hatred that we suffer from today in the US.
Cold war refers to a general rivalry based on political ideology and attempts of USA and USSR to dominate the world. There were no specific actions of USA government that could be viewed as specific part of the cold war. All general policies and actions of USA, after World War II and lasting upto 1970's, in the area of foreign relations and defence including arms build up, were way part of the cold war.
The following of such action of USA can be considered to be most harmful to the interest of the American society.
- In general arms race that diverted resources of the country from application that could benefit the country economically.
- Unnecessary poor relations with country in name of political ideology. This also hurt the US trade and economic interest.
- Unnecessary harassment of American citizens on suspicion of being communists. Such action sometimes forced eminent US people to leave the country and settle elsewhere. For example, because of such actions by the US Government, Charlie Chaplin was forced settle in Switzerland in 1952.
- Involvement in war in other countries, particularly Korea and Vietnam.
- Straining of relationships with Cuba. Bay of Pigs invasion represents most dramatically the casualness with which US has handled its relationship with Cuba.
- Support to wrong kind of people in other countries. For example US played an important role in supporting Osama Bin Laden which enabled him to become powerful.