While this question has been posed and answered by other editors on eNotes (see links provided below), there are other examples of irony that have not been addressed as of yet.
Arthur Miller's play, "The Crucible," has two very specific aspects of irony.
First, the fact that Reverend Parris is more worried about speaking to his congregation about gold candlesticks, the ownership of his congregation owned house, and his wages is ironic given that he is a Reverend. A man of the church should not be worried about his money, or ownership, or preaching about himself. Instead, he should be worried about bringing people to God--what he devoted his life to.
Second, John Proctor's behavior is very ironic when it comes to accusing Abigail of lying to the courts. When Elizabeth tells John that she thinks he needs to tel the courts about Abigail's admission to him that no witchcraft was involved, John questions going because of he is afraid that his own sins will be revealed. The fact that he does go to expose Abigail is ironic given his own sins. Think of it in this way, John is calling the kettle black" when accusing Abigail of not being a good Christian. He cannot possess that title either.
One last and final irony seen in the play is when those who are being accused are the ones who are "higher up." It is not until the wives of judges are accused that the court begins to look at the real evidence being presented. When, and only when, more high profile people are being accused of witchcraft is when the courts readjust their questioning and proceedings.