I think the morals in Salem did spoil. Guilt, anger, revenge, and lies stunk up the whole place.
If you are wondering why the Rebecca Nurse and John Proctor type characters were able to keep their moral compasses in check, then I think you could argue that these two were people who believed in their God and had agreed to live according to the disciplines of the bible. They both made conscious choices to live according to telling the truth, and they suffered the greatest price for it unfortunately.
This is why The Crucible is such an important piece though. It demonstrates that a society can go overboard with the effort to live according to rules and it is important to consider the truth and how people really treat each other.
The answer to this can be found before the actual action of the play starts -- it is in the notes that Miller includes before Act I starts. According to Miller, it was "hard work," rather than the Puritan religion's creeds and beliefs, that prevented the morals of the people from spoiling.
What Miller is saying here is that the people acted properly because they worked hard. In the rest of the paragraph after Miller says that hard work kept their morals from spoiling, he says that they had to spend all their time working hard and so they did not have time to go around doing immoral things.