Initially, John Proctor's dilemma has to do with repairing his broken marriage and staying away from Abigail Williams, the young woman he had an adulterous affair with while she worked in his home as a servant.
Proctor tries and tries, for several months to win Elizabeth's trust back, but to no avail. She is distant and formal with him when we meet her in Act II. Proctor pleads with her to accept the fact that he will not stray again. But his wife has a hard time trusting him, when he returns home late she believes that he has spent time with Abigail.
When he tells her that there was no witchcraft in the forest and that the girls were just having fun, and Elizabeth finds out that he was alone with Abigail, all her fears are renewed.
It is in this atmosphere that Elizabeth is arrested. His dilemma changes completely from a private one between he and Elizabeth to a very public one, his private life is exposed and his credibility and dignity are put on trial.
Proctor bares his soul in the public arena, the court, in an effort to save Elizabeth's life.
I think that you are asking how John Proctor's problem changes throughout the course of the play. If this is what you are asking... In Act I it is clear that one of Proctor's main problems is that he mistakenly had an affair with Abigail, which he now seriously regrets. Because of the affair he feel horrible for what he has done to his wife, and out of jaelousy, Abigail has now accused Elizabeth Proctor of witchcraft to get her "out of the way".
Another problem that Proctor has occurs in Act III when he is accused of witchcraft by Abigail and the other girls. Fed up with the way the court is proceeding and the fact that he does not want his wife to die for his sins, he calls Abigail out in front of the court and tells the truth about the affair. To this, Abigail and the other girls eventually accuse John of witchcraft. In Act IV, he begins by confessing to witchcraft to save his life but then decides that the only right thing to do would be to tell the truth and be hanged for not confessing to witchcraft.