In some ways, Hale does not change from act 1 to act 3. When Hale arrives in act 1, he is borderline arrogant in his ability to find the Devil's presence in Salem and rid the town of witchcraft. He is 100% confident in his ability to read the situation and act upon it.
By act 3, Hale is still a man that has strong convictions and is willing to act on his personal beliefs and values. The difference is that Hale no longer believes there is actual witchcraft going on in Salem. He is fully confident that the court is being manipulated by Abigail and the other girls, and it is for that reason that he quits the court. His attitude about the witchcraft in Salem has completely changed, but Hale is still a man that believes in acting upon the evidence that has been put before him. That is why he is so keen on examining the girls and even John and Elizabeth Proctor.
His methodology is quite scientific, but by act 3, Hale's tests have failed to yield solid, supporting evidence to the presence of witchcraft in Salem. Due to the lack of evidence on hand, Hale believes that the court is acting foolishly. He is unable to convince the court officials of this, so he quits the court. Hale changes his beliefs about witchcraft in Salem, but he acts upon his personal convictions to do what is right throughout the play.
Reverend Hale undergoes a dramatic transformation between Act I and Act III. Arriving in Salem as an authority on witchcraft, he becomes a vital member of the court, assisting in the process of uncovering witches that are present in the village. Reverend Hale participates in the condemnation, along with the court, and signs off on the execution of 12 people.
As the play progresses, particularly after John Proctor is arrested, Reverend Hale begins to see that the accusations of witchcraft are being used as a tool of vengeance in the town. He begins to doubt Abigail Williams testimony and when she is revealed to be a harlot, for having an adulterous relationship with John Proctor, Reverend Hale no longer believes that there are any witches in Salem. He leaves the court and returns home.
At the end of the play, Reverend Hale returns to Salem with one purpose and one purpose only, to save as many of the accused as possible. He goes about this process by begging those awaiting execution to confess to witchcraft in order to save their lives.
His change has occurred as a result of a long period of meditation and fasting, he believes, now, that he is actually working for God, by trying to save innocent people from wrongfully being put to death for a lie. He particularly wants to save John Proctor's life, but is unsuccessful.
When the reader/audience is first introduced to Reverend Hale in Act 1, he has come to Salem for the purpose of finding signs of witchcraft in the village. He brings with him books containing knowledge of how to find these signs and is detrmined that no witch in Salem will go unnoticed. In the beginning of Act 2, he seems to be just as determined to help the court when he goes to the Proctor's home to question/interrogate them on their religious ways and their belief in witches. When Act 3 comes about, he begins to change as he sees the way that the trials are being conducted -- the good and respected people of Salem who have been accused (or who have relatives who have been accused) are not allow to defened themselves or present evidence to free themselves. The court only listens to the girls and this causes Hale to realize that the courts are not being run the right way. At the end of Act 3, Hale sees Mary Warren and the other girls accuse John Proctor, and Hale then quits the court because he does not believe that the girls are telling the truth and thinks that the accused are being ignored.