There are many conflicts in this play. Several of them stem from the politics involved--both in the time the play is written and the time the play is set. The witchhunt is symbolic of the hunt for communists in the 1960's in the US as well as the literal hunt for witches in Puritan New England.
The Puritans were very unforgiving, and there is little wiggle room for correcting a wrong judgment. This leads to the inevitable death of Rebecca Nurse, her husband, and John Proctor--three of the most respected and level-headed people in the town. Even though considerable doubt had been cast on the girls' testimony by the end of the play, the hangings had to go on as planned since the sentences had been passed.
In addition, the society left no room for human nature. Abigail and John are victims of human nature and temptation. This leads to the conflict between John and his wife and also between Abigail and Elizabeth. As a result, Elizabeth is accused of witchcraft.
The Putnams are also guilty of stirring trouble in the community. Mr. Putnam is greedy and attempts to acquire land or simply to claim land to which he has no legal right. Obviously this would cause conflict with those who have rightful claim.
Goody Putnam is jealous of women whose children and grandchildren have lived when hers (except for Ruth) have all died. Rebecca Nurse in particular is targeted since she is also a midwife.