Something else that came out of the 20's was the involvement of women in influencing the country and the government. Prohibition was largely a result of the Temperance Movement which started years ago.
An important negative effect of the 1920s was the enacting of Prohibition, which opened the door for organized crime to make tremendous profits and, thereby, expand. For instance, Al Capone of Chicago had a notorious gang that made huge profits from bootlegging. Among many negatives, Capone's powerful gang exerted influence upon municipal officials, causing corruption in the city. Detroit on the Canadian border, was also a site of great corruption. Certainly, Prohibition did more harm than good as it gave rise to proliferate illegal activity. (Even Joseph Kennedy, father of the 35th president of the United States made much of his early fortune as a bootlegger.)
I think that decade showed us what we were capable of economically, and also warned us about restraining that potential in sensible ways. The economic expansion and the growth of the middle class was amazing and breathtaking at that time, and we saw a standard of living we'd never seen before. The Depression that followed finally shocked us out of any belief that a laissez-faire approach to the economy was foolish at best, and we have never strayed back to that approach, or at least, not really until recently.
The 1920's reflected a strong reaction to the horrors of World War I. Previously, there was the belief that society was "progressing," hence the Progressive Era; however this all crashed down as a result of the war.
Among the many changes, a return to intense patriotism, indicated by the rebirth of the Ku Klux Klan which redirected itself to a campaign of "100% Americanism." The new patriotism took the form of "Nativism," and resulted in the passage of the Emergency Immigration Act, which severely limited immigration from Eastern and Western Europe, and all but eliminated immigration from Asia. Prohibition came to the forefront during this time; largly as a result of the war, since most breweries were of German origin. Also, Fundamentalist religion became intensely popular. All of this represented a "back to the basics" response.
There were positive changes, including the Harlem Renaissance and the birth of Jazz as an art form. It was also during the twenties that women were given the right to vote. The Harlem Renaissance was itself a product of the Great Northern Migration, when many black families moved north in search of opportunity.
Different people can have different opinions on this. My own opinion is that the most important effect of the 1920s was that it started America on its way toward having a split culture -- one in which there were traditionalists (often rural) who were suspicious of the "modern" people (usually from the cities).
In the 1920s, the traditionalists felt that the United States was going the wrong way. They felt that there were new values (jazz, flappers) that were taking over the cities and the popular culture and that these values were destroying the good, traditional American way of life. They even worried about people going away from biblical teachings in favor of ideas like evolution.
All of these worries can still be seen today. I am not saying that there was a direct connection between the 1920s and today, but the divisions that showed up in the 1920s are mirrored in our current society and, I would argue, the divisions of the 1920s helped to shape the arguments that we have today over social issues and values.