The incident of Caterina Sforza's eldest son being held hostage occurred in 1488 after the murder of her first husband, Giralomo Riario. Eye witness accounts differ as to whether or not she hiked her skirt, showing her genitals and saying she could always make more kids.
The castle of Ravaldino was inside the city walls of Forli, not on the edge of the city as shown
Juan Borgia never besieged Forli and Ravaldino castle. The city of Forli was taken and Ravaldino besieged by Cesare Borgia in December and January of 1499 (The new year of 1500 did not start until March prior to the adoption of the Gregorian calender many decades later)
Lucrezia asks Juan if panthers are common in Spain and he cryptically replies "not anymore". If he means captive panthers, he's wrong, because they were common in Spanish menageries of the time. If he means wild panthers, he's technically right, but panthers (i.e. cave lions and leopards) went extinct in Spain in the Paleolithic and there is no way a 15th century man like Juan could know that.
The shock displayed by the audience when Juan unveils the jaguar, which he calls a panther, is unlikely. Romans had been familiar with leopards for hundreds of years at this point, which they called panthers, and these animals don't look very different from jaguars.