1963
While society has been slowly changing since the Industrial Revolution, and the civilization and growth of our nation has gradually turned us from a rural nation to an urban one, with the focus of society more on collectivism than the individualism needed (and preferred) for a rural society, I believe the one major tipping point for the last half century would be the 1963 assassination of President Kennedy, and particularly the aftermath.
After the initial shock wore off, the nation wanted answers, and the only official answers we got was the report from the Warren Commission. And that report did not provide enough (or according to some, the right) answers. This led to a general feeling of distrust in the honesty of the Federal govt, which had never been felt before. Even though many people still believed that our govt was always working in our best interest, and had always done so, so many people felt that there were things they knew, but would not tell us that a general feeling of suspicion began to develop. Where as before, our govt, which had won WWII, and was protecting us from the Russians (communism), the idea that they were deliberately misleading us began to become part of the popular culture. It didn't happen overnight, but it did happen.
Aided by the news media (who felt the same way), everything the people in govt did became targets for closer scrutiny than was customary before. The Vietnam war, and the news media, for the first time being able to bring the war into America's living rooms every night played another large part. The mishandling of the Vietnam War (fighting without any clear idea of achieving a victory) further increased the people's dissatisfaction with our govt. The Peace movement, and the counterculture revolution of the "hippies", the popularized use of recreational drugs, the govt's often heavy handed and cruel attempts to control the people, the civil rights movement, all were ingredients in the stew that has fermented for the past 40 odd years leaving us with the stinking rotten mess we have today.
There is no one point anyone can point to and say "Here is where it all went wrong", only numerous points where one can say "Here there was a change, greater than before". Some of the changes were large, and others small, but all had effects that grew and changed over time.
Somewhere in our law schools the idea that "better 10 guilty men go free than one innocent man be hanged (or go to jail) became the popular standard, and eventually came to be the accepted "proper" ideal. Lawyers, judges, and even politicians trained to this standard came to dominate our legal and political system. A hundred plus years ago the idea that "if we hang an innocent man every once in a while it is tragic, but it is the price we must pay for getting the guilty, and protecting society" was the popular and proper ideal. That has changed.
Another contributing factor in the past century has been the growth of the insurance industry. I am not against insurance as a concept, it is a pretty good idea, generally, BUT, one real world consequence of the power and wealth of the insurance industry has been the idea that since insurance will replace or compensate you for stolen/damaged property, you ought to have insurance, so you were no longer justified in defending your property. Over time, we generally lost the legal right to use (deadly) force to defend our property, which had always been recognised before. We didn't hang horse thieves and cattle rustlers because horses and cattle were as important as people, but because they were people's livelihoods. And outside of neighbor's and church charity, there was no replacement. If you stole a man's money, you went to prision. If your stole his plowhorse, you took away his means to grow food, and more. You went a long way towards killing him and his family, and it was considered a much more serious crime, so when caught, you hung. After insurance companies established themselves, it became more morally acceptable to pay a portion of your hard earned wages, for your entire life, to an insurance company rather than defend your property (including your money!).
While made into popular heroes for the entertainment of people who were never affected by them, the bank robbers and train robbers of the Old West were hated by the ordinary folk, because they stole their life's work, and there was NOBODY who would replace that! That is why ordinary folk formed posses, and one some occasions fought it out with the bank robbers in the streets (such as Northfield Minn), to protect their money. There was no FDIC to replace your money, when the bank got robbed, your life savings were just gone, and gone forever!
The Great Depression, and Prohibition were other huge turning points, affecting how the people felt about how govt handled our lives, and the reason why moonshiners and even bank robbers became popular icons, because these people were beating the system. Even though bank robbers stole from us, they were daring glamorous figures, at least for a time.
WWII, and later the Cold War brought the country back closer to being content and trusting of our govt, but not completely, as not all of us forgot what our Founding Fathers knew.
FDR pushed this country further on the path of socialism than anyone before (basically prohibiting common ownership of automatic weapons and personal ownership of gold, among a host of other things), and had it not been for the insanity of the Second World War, and the US role in winning it, I believe FDR would not be considered by history as the great man he is often regarded as today.
I could go on, but there are nearly as many views of where we went wrong and right as there are people. Your question has no simple easy answer, only that our situation today came about as a result of the best of intentions, and the law of unintended consequences.