In November 1478, at the request of Ferdinand of Aragon and Isabella of Castile, Sixtus IV issued the bull Exigit sinceras devotionis affectus, permitting the Spanish crown to appoint inquisitors in its own territories. Inquisition tribunals had existed in the medieval church for two and a half centuries, but this one was different in a way that mattered: the crown, not the papacy, named and controlled the inquisitors. Within four years reports of its severity against conversos, Jews who had accepted baptism, reached Rome, and in April 1482 Sixtus issued a brief protesting that the tribunal was proceeding on the testimony of enemies and slaves and imprisoning the innocent. Ferdinand refused to accept the correction, and the pope, needing Spanish support elsewhere, did not press it. The institution he authorized outlived him by three and a half centuries.
The second decision was doctrinal in form and financial in effect. The bull Salvator Noster of 1476 extended the benefit of an indulgence to souls already in purgatory, obtainable by the living on their behalf. The reasoning drew on a developed theology of the communion of saints, but the practical result was a new and highly saleable category of pious giving, and it is a direct ancestor of the preaching that provoked Martin Luther in 1517.
Against these stands a decision of a different temper. The Immaculate Conception of Mary was fiercely disputed between Franciscans and Dominicans in his day. Sixtus approved a feast and office for it in 1476 and then, in 1483, forbade either party to accuse the other of heresy for the position it held, leaving the question open for another three and a half centuries.