The show depicts Giuliano de Medici's son as being the illegitimate result of a one night stand, with Giuliano only discovering he was to be a father as he lay dying. In reality, Giuliano's son, the future Pope Clement VII, was born only a month after Giuliano died. His parents were considered to have been betrothed and so Giuliano's son was considered legitimate.
The show depicts Niccolo "Nicco" Machiavelli as a teenager. However, at the time of the events depicted in the series, Machiavellia was only nine years old.
The name of the de Medici's is consistently mispronounced. The stress is on the first syllable (Me-).
Binoculars are treated as an existing gadget, but were actually invented a century after Da Vinci died.
The real Lorenzo de Medici had no problem conceiving a son. The low-class mother of his illegitimate nephew would be a nameless nobody and definitely not find herself at the head of the Medici family fortune.