What is Hale's mission in Act IV?
When Hale came to Salem, he came thinking that he was going to help the town and investigate whether or not the town is afflicted by witchcraft. Though he has never actually seen a witch, he's read many books about them and feels confident he knows all the signs and indicators. However, he never stops to think that people may lie.
In Act IV Salem has returned to Salem. Remember, at the end of Act III he "quit the court" and left Salem. When he quit, he finally realized that the court was not being impartial and was not listening to to the presented evidence, so he left. When he returns, he tries to atone for his previous actions my counseling the charged citizens to confess. While he no longer believes they are guilty, he does believe that "counseling them to lie" is the only way they will live. Even as Proctor, Rebecca, and Martha are being led to the gallows, he's still pleading with Elizabeth to get John to save his own life by confessing.