There is a conflict between Reverend Parris and much of the community, including John Proctor and Giles Corey. Parris is especially nervous about learning what Abigail, Betty, and the other girls were doing in the forest the night before because he believes his "enemies will [know], and they will ruin [him] with it." Further, he believes that his "ministry's at stake, [his] ministry and perhaps [Betty's] life."
There are also hints of a conflict between Abigail Williams and Elizabeth Proctor. Parris asks Abigail about her reputation in the town, implying that it might not be as spotless as it should be. Moreover, he says he's heard that Elizabeth has said that "she will not sit so close to something soiled" and this is the reason she doesn't attend church.
Likewise, we also see the conflict between Mrs. Putnam and Rebecca Nurse (though it is really a one-sided conflict). Mrs. Putnam is angry with Rebecca because, while Putnam has lost seven of eight babies, Rebecca has never lost either a child or a grandchild. It seems colossally unfair to Putnam, and she holds a grudge out of bitterness, claiming that there must be some conspiracy working against her, that "There are wheels within wheels in this village, and fires within fires!"