This is an interesting question because whenever I think of the concept of a scapegoat I think of the ways a scapegoat was meant to heal a society. Among the ancient Hebrews, a goat was allowed to escape into the wilderness as a symbol of atonement for the sins of the people:
But the goat chosen by lot as the scapegoat shall be presented alive before the LORD to be used for making atonement by sending it into the wilderness as a scapegoat. (Leviticus 16:10 NIV translation)
These days, though, it seems like we hear more and more about people becoming scapegoats for various things. In America, in particular, our political leaders or the government become scapegoats for everything that is wrong with society. If we can't find a job, gas prices are too high, or our health care system doesn't work the way we would like it, we make the President, or Congress, or the Government a scapegoat and send them back into the wilderness of our society heaped with the sins of their failure.
When scapegoats are used in this way, they harm society because they allow society to make, en masse, an ad hominem attack on one individual or an ad populum attack on one group of people. Instead, we should sit down, think about our problems, and try to come up with solutions. It is much easier, however, to blame others when things go wrong rather than working out solutions or accepting responsibility ourselves.