A blog from 2012:
The Borgia miniseries has highlighted some of the technological advances of the Renaissance, to its credit. The writers haven't always gotten the details right, but they are good at showing the essence.
Take the advances in warfare of the time. The cannon figures heavily in the second season, for good reason. By the Borgias' time, iron shot and better gunpowder produced cannons that could smash through city walls like dry bread. Yet they were still uncommon. So when Cesare Borgia began the systematic retaking of the Papal States with seventeen cannon in tow, he had the Renaissance equivalent of the atom bomb.
The Showtime Borgia miniseries also touches on the first use of smaller guns. In the completely fictional scene where Il Moro rescues Caterina Sforza from the clutches of Juan Borgia, there is an equally fictional glimpse of Il Moro's army brandishing the forerunner of the musket, the arquebus. The guns look right but they are held wrong, and they repeat fire which is centuries in the future. The first arquebuses were more like mortars than muskets, meant to stand on a tripod or hook to a stationary object ("arque" means "hook"). They were heavy and unwieldy, so Il Moro's men could not have held them like spears. But the first battle featuring a squadron of arquebusiers happened right around that time, a portent of the future. So the Showtime series is right to showcase the arquebus.
Another Renaissance innovation was double entry bookkeeping, as noted by Lucrezia, Vanozza and Giulia in the completely fictional account of their campaign to end the accurately portrayed corruption of the cardinals of the Church.
The miniseries so far has not focused on the enormous effect of the printing press on the Borgia family, which came to power roughly sixty years after its invention. Rome had a number of presses by the time Alexander was pope, and his enemies used them effectively.
For example: the rumors of incest between Lucrezia and her father and brother had their genesis in a spiteful letter written by her first husband, Giovanni Sforza, to his cousin Cardinal Ascenio Sforza, complaining that the pope would not send Lucrezia to him because "he wants her for himself." The Italian verb, "to want," has the same ambiguities as its English equivalent. Whatever Giovanni Sforza meant, rumors soon accused the pope and his daughter of incest, then enlarged to include Cesare as part of an incestuous triangle.
In an earlier era, the rumors would have died out rapidly. But Roman poets–the yellow journalists of their time– sold sheets of doggerel about the alleged incest, which were a big hit with the Roman public. Written texts like the Bible had been revered for centuries, so people may have believed what was in print (much the way the public treated internet rumors in the early days). And what was rumor went into the "histories" of the time as fact.
The Borgia miniseries has to date ignored this nasty rumor, to its credit. Ignoring the printing press, though–that's a big omission.