Dishonesty is the root of every major conflict in Miller’s The Crucible. While the authorities of the court demonstrate moral failings akin to dishonesty, it is the lies spread by the people of Salem themselves that stand as cause for the trials in the first place. And it is the lies of Salem citizens that keep those trials going.
When you look at the many examples of dishonesty in the play (the deceit of Abigail and her friends and the disingenuous behavior of Danforth and Parris), you may discover a number of through-lines connecting these examples. The thesis you choose as your argument will depend on (1) which of these examples you find most interesting and most important to the story and (2) the specific constraints of your writing assignment.
The most fundamental deception in the play comes from the girls of Salem, who lie in order to protect themselves from punishment after being caught dancing naked in the woods at night. This evasion of punishment leads to a cycle of lies that grows increasingly pernicious.
Abigail connives to have Elizabeth Proctor arrested for witchcraft and Elizabeth’s best hope for exoneration fails when Mary Warren finds herself incapable of exposing Abigail’s lies. Thus, Mary Warren perpetuates the cycle of lies and effectively condemns Elizabeth to death (though, as we know, her pregnancy gets her released from custody later).
Focusing on the dishonesty of these girls, you could write about the ways that dishonesty becomes an escalating cycle in the play. You might also look at how deception is motivated by differing impulses, from evasion to vengeance.
Alternatively, you might focus a paper on the more subtle dishonesty of the characters that do not lie, per se, but instead refuse to honestly review the facts before them. Danforth’s dishonesty stems from his refusal to accept the truth that is so clearly presented to him, preferring to maintain the reputation of the court. Such an approach to justice makes the court itself dishonest, enforcing a vision of itself instead of working for fairness and truth.
Proctor: laughs insanely, then: A fire, a fire is burning! I hear the boot of Lucifer, I see his filthy face! And it is my face, and yours, Danforth! For them that quail to bring men out of ignorance, as I have quailed, and as you quail now when you know in all your black hearts that this be fraud—God damns our kind especially, and we will burn, we will burn together!
In the final act, Danforth speaks directly to this point.
"Twelve are already executed; the names of these seven are given out, and the village expects to see them die this morning. Postponement now speaks a floundering on my part; reprieve or pardon must cast doubt upon the guilt of them that died till now."
Danforth effectively chooses to commit fraud rather than admit that the court has been wrong in its actions.
Finally, you may also consider looking at how John Proctor and Reverend Hale each come to terms with their own moral failings, their deceit and their self-deceptions. This act, for each of them, brings some kind of personal redemption although it does not necessarily win the day. Proctor is honest with his wife, yet she continues to be cold to him. Hale repents of his role in the trials, but it is too late to stop more innocent people from being killed.
Importantly, however, these characters do the hard work of being honest when dishonesty is the easiest thing. Thus, these two characters are examples of both dishonesty and honesty. The play offers a complex view of moral integrity, especially with Proctor and Hale.