What are similar ideas between The Catcher in the Rye and The Crucible?
The original question had to be edited down. I would suggest that one specific theme that both works share is their mutual lack of trust in authority figures. In The Catcher in the Rye, authority is shown to be something that is insincere. It is more interested in substantiating its own power and control as opposed to looking out for the common good. Holden's mistrust of authority is representative of the hypocrisy he sees in it. Holden refuses to simply trust in authority as he is convinced that personal ambitions and personal desires underscore all positions of power, as seen in his treatment of the leadership of Pencey or in his perception of Mr. Antolini. This would be applicable to Salem in Miller's work. The individuals in the position of power are there to consolidate their own control over the town's affairs. Parris, Hathorne, Danforth, the Putnams, and Abigail are concerned with how the pursuit of witches can advance their own agendas and position of control in the community. The pursuit of truth is secondary. Miller shows authority as one that is concerned with its own substantiation and its own desire to maintain control. Holden's lack of respect for authority is something that is mirrored in the characters of The Crucible who are forced to speak out against the injustice that they see perpetrated by those in the position of social, religious, and political power.
I would also suggest that another common link to both works is how the outsider is shown to be something towards established society shows disdain and scorn. The world in which Holden inhabits is one that has little tolerance for those on the outside. The ending of the novel in which Holden is in an institution is reflective of this. Such a social setting is one in which voices are not acknowledged as much as silenced if they voice dissent. This exclusionary view of society is akin to Salem during the Witch Trials. The initial victims of the accusations are outsiders like Sarah Good or Tituba. Over the course of the drama, more people like Rebecca Nurse, Giles Corey, and Proctor, himself, are imprisoned and executed because they are on the outside of established society. Salem holds disdain for those who speak out, punishing them severely for disrupting the view of establishment figures who wish to carve out society in their own perception. In both works, those on the "inside" are there because of power and it is this power that compels them to punish and silence those on the "outside."