Danforth pushes for the accused to be hanged. Is Danforth guilty of murder? Consider elements from the text, as well as the idea of spectral evidence

No, Danforth is not guilty of murder.  He is perhaps guilty of excessive zeal and bad judgement, but not murder.

Danforth is basing his decisions on evidence that has persuaded most of the town of Salem.  He is caught up in the same sort of wave of emotion and fear that they are -- the kind of thing that makes people believe in the spectral evidence of the group of girls.  Yes, he is also motivated by a desire to maintain the dignity of his office and the court, but that's not all that's going on.

Danforth probably should have acted differently, but so should the whole town have.  He is not any more guilty than they are.