Several days after the professor is kidnapped, the police and Father Brown investigate the scene. Father Brown picks up a handkerchief and announces "Chloroform". However, any chloroform would have long since evaporated leaving a simple handkerchief.
Father Brown twice says that the rosary's female owner "took Holy Orders", which means to become a priest, and is considered a sacrament in the Catholic Church. Women do not become priests in the Catholic Church, either at that time or in this. He wanted to say that the woman became a nun, and should have said she "entered a convent" or "took vows". This is entirely different from Holy Orders, and it is impossible that a Catholic priest would make such a mistake.