One irony in the third act occurs when Proctor has confessed to his affair with Abigail, saying that the affair proves she is motivated by dishonorable and dishonest impulses in accusing Elizabeth.
The court wants corroboration on this claim and so calls Elizabeth to confirm or deny Proctor's confession. She lies. She says that there was no affair.
This moment is ironic because Elizabeth believes she is saving her husband by lying when in fact she helps to cause his arrest and fails to save herself. If she had told the truth, the trials may have come to an end and Abigail would have been recognized as a fraud. Yet, Elizabeth lies for the only time in the play, thereby condemning herself (an innocent person) and her husband (an honest, innocent man).
Another irony comes in Mary Warren's confession. She confesses to faking the experience of seeing spirits. When she confesses this truth she is not believed (an irony). To defeat her confession, Abigail leads the other girls to fake the experience of seeing Mary Warren's spirit sent out to them. This is another irony, as Mary Warren has confessed to the absurdity of this act and its falseness, yet it defeats her and she once again is made to agree with the lie and recant the truth.