The siege is presented as a battle between Catholic Christianity and Turkish Islam. In the real war there were Protestant, Eastern Orthodox and Muslim states and mercenaries (including a small number of Turks) supporting the Holy League and Christian states supporting the Turks. The Principality of Wallachia, an Orthodox Christian vassal state of the Ottoman Empire, secretly sabotaged the Turkish siege and was providing intelligence to Austria.
Marco d'Aviano is shown meeting Emperor Leopold I for the first time immediately before the siege in 1683. Marco had actually been a confidant and adviser to Leopold since 1680.
The Holy League derides Jan III Sobieski as being a "mere general" and unfit to lead the combined armies as he was not of noble birth. In fact the House of Sobieski had been a prominent noble family since the 15th century. As well as King of Poland, he was Grand Duke of Lithuania.
The ferula used by Marco D'Aviano (a friar) is completely anachronistic, as it was created by the Neapolitan sculptor Lello Scorzelli (1921-97) and used for the first time in 1965 by Pope Paul VI on the closing day of the Second Vatican Council (1962-65). It is widely associated with the pontificate of John Paul II. However, only popes are allowed to use the ferula.
During the Battle of Vienna, the Bruges Bell Tower is occasionally visible. The Bruges Bell Tower is obviously in Bruges, not Vienna.