I would say the documentary is a very dramatized version of the narrative in general, with few distortions and mistakes, I suppose for the sake of drama.
You should remind that the Conquest or the Fall of Constantinople is not very well-known especially in detail. The reason was that historical sources or chronicles are very weak, especially in the Turkish side. It was not common among Turkish chroniclers to write about a siege or battle in detail since they found it boring for the audiences. So, I cannot say that there is huge huge mistake that cannot be overlooked, but I am not satisfied what I watch.
For people who had seen the show, a few problem that I find:
- Mara Brankovic, was the wife of Murad II between 1435 and 1451 and yes, it is known that she and young Mehmed had good relationships because Mara did not (or could not) have a child and after Mehmed lost his biological mother they had a very close relationship, but I don't understand why on Earth one would imagine her as a leading figure in the Siege. I relate this the lack of women figures in the historical narrative. Most probably, producers needed some strong women characters and Mara was useful because it is known that she was close to Mehmed and an Orthodox Serbian princess and most importantly it is certain that she existed.However, her character actually built on a real Ottoman scholar, known as Akshamsaddin, who is actually one of the few figures we can prove with first hand archival document since there is a famous letter from him to Sultan during the Siege that consulted NOT to end the Siege and push on. While Mara Brankovic became the advisor of Mehmed II, the real consultant and advisor and a shrewd scholar, Akshamsaddin, who was also an important religious figure who was told to discover the famous tomb of Eyyub al Ansari, the companion of the Prophet, in Istanbul somehow miraculously, was gone.
- The general character of Mehmed was built according to narratives and sayings, but historically speaking it is not certain that what kind of a man Mehmed in reality. It is known that he was very young, around 21 at youngest, and a good educated, clever man. Idealization of Alexander the Great, however, is a dramatic move. In general, only a few Ottoman prince and sultan are known personally that much. It is said that he could speak Italian, French, Arabic, Persian and Greek. It was not uncommon among Ottoman sultans to speak Greek, but I don't believe there is any serious historian could say he spoke all those languages without hesitations.
These two are the most important problems I could find. There are also minor issues. For example,
- It is not clear that Candarli Halil Pasha had personal interest in Constantinople, or he was a corrupt man. Some think that he might have been a cautious stateman, and he was rightly so. Taking Constantinople was always a dream for Ottoman sultans, but in financial realities, I can assure this that Mehmed made great financial losses, both in the siege and after restoration processes after the siege. Ottomans needed a bold man who could ignore this aspect. Mehmed was a dethroned sultan, he needed a move that could prove his greatness without any hesitations.
- Outfits, weapons and musics of Ottoman army is a very modern image and it is not widely known what they were wearing or playing. So this is not a mistake, but a necessity .
- Most interestingly, producers did NOT use some very dramatic scene that were somehow reported in the historical documents. For example, there is a very dramatic moment in which Mehmed II climbed up the Hagia Sophia and wept when he saw how his own soldiers sacked the city and ended the Sack two days earlier by taking the risk of pissing off the Janissaries.
- There is a moment when three or four Genovese ships managed to arrive the city, he rode his horse into the Bosphorus and people around him stopped the Young Sultan very hardly. He was so angry that he slapped Baltaoglu Pasha in the face.
- Some reports claim that he did not killed Lukas Notaras directly, but actually made him as the governor of Istanbul in the beginning!