Pope Alexander refers to Cesare as his "only son," given that Juan is now dead. Yet the pope had a third son, Gioffre/Joffre, who was present in Season 1 and then dropped out entirely without explanation. In real life, Gioffre outlived his father.
When sent to the Castle de San Angelo and locked up, the cardinal mentiones the 'Iron Maiden' as a torture device. This device was developed centuries later (19th century).
During his discussion on the stairs with Vanozza, the Pope refers to himself in the singular with "I" and "me", rather than in the plural with "we" and "us". This is the first time he uses those pronouns since he became Pope.