When Da Vinci is approached by Lucrezia from behind, he pulls a sword and points it at her with his left hand. In the next shot he has somehow turned around and is now pointing the sword at her with his right. After a couple of lines, Da Vinci lowers his sword and his position has changed again. Now the the sword is back in his left hand.
While conversing with Verrocchio in Cosimo De' Medici's grave room, Leonardo envisions the heavens. In the graphic display, the Sun is seen at the center, and Earth and the Moon revolving around it. However, it is not until S02E04, wherein it functions as a major story point, that Da Vinci conceives of the idea of a heliocentric system - before then, he would presumable have taken the Sun to be circling the Earth.
The Castel Sant'Angelo is depicted with the bronze statue of St. Michael the Archangel on its roof that is seen in the present. That statue did not exist in 15th Century Rome, it was erected on the top of the castle in 1753.