I would say that the issue of how to effectively deal with adultery is still present. Proctor's fundamental dilemma is how to reconcile with his going outside the realm of marriage. It is addressed on both a social level and on a personal one. Miller does a wonderful job in showing how the effects of adultery linger, as there are insinuations and statements from Elizabeth in the beginning that she believes the scent of stray is still there. Proctor's battle to reconcile how to be a good husband with the reality of having made mistakes as any husband broach the larger issue of witchcraft accusations that he has to face down the road of the play. In his resolution, he finds a way to derive moral ascendency in both domains. I would say that another element of the play that is evident today is the idea of manufacturing accusations. Abigail's craft at concocting stories and deception following deception is something that we see in play today as individuals are as savvy in understanding how to manipulate the media and others in making sure their perception is out there and that others share it. The idea of individuals lacking the moral or political will to challenge these assertions is also present today, as well.
The Puritan work ethic of the time is still very evident today. Puritans in 17th century Salem believed hard work kept the devil away. In the modern day, Americans work more hours per week and take less vacation than almost any other society on Earth.
The Puritans were fundamentalists on the Bible and Christianity. While there is no organized Puritan Church these days, there are many variants of fundamentalist Biblical Christianity, and the country on the whole is still quite religious.
One could also argue our society is still very reactive to fear, and are willing to ignore civil liberties and legal rights in exchange for at least the perception of security. In Salem, they were willing to sell out innocent friends to save their own skins. Today, Americans are willing to give up the free speech and association rights of their countrymen in order to apprehend terrorists.