The Pope of the Catholic Church during the majority of the Spanish Inquisition was Pope Innocent VIII, who had originally appointed Torquemada as the Grand Inquisitor of Spain in 1487. Unlike the film, which portrays the Pope as disapproving of Torquemada's actions, Innocent VIII fully supported the endeavor.
Mendoza has holes in his palms from when he was crucified. However, people being crucified were nailed to the cross through their wrists, not their palms: the palms not being strong enough to support the weight of a human body.
Being carted away for burial, Maria is obviously breathing, which should have been noticed by the people around the cart.
When the rats swarm over Antonio, several of them are pressed hard up against his chest and arm. When he reaches out to grab the dead rat, these rats do no move at all, indicating they are dummies.
Torquemada uses a pair of pivoted scissors to cut out Maria's tongue. The movie is set in 1492, and pivoted scissors were not manufactured until circa 1760. (In 1492, Torquemada would have been using spring shears.)