Artistic License History / Magnificent Century: Kösem

• Most of the plot points in the series could be sorted into two categories - one that we have no way of knowing whether they happened (such as Safiye's death - we don't know when she died or how), because the historical record is incomplete, or ones that there's no way in hell they happened. Many of Safiye's most egregious exploits fall into this category - she dissapears from historical record after Ahmed's ascencion, when she was exiled into Old Palace. Considering how unpopular she was with the people and that she was responsible for the death of sultan's older brother, this was pretty much given and though she may have tried to gamble her way out of exile, there's no way we can prove it, and for the most of the period the series is set in she probably didn't do much except for enjoying the retirement. The series understandably didn't want to waste a good character and actress, so they gave her more and more implausible things to do, up to and including secret surviving son.
• Mehmed III. and Safiye had two daughters with Safiye, possibly three, and one of them was named Hüma, though she was older than Hümaşah in the series. Mehmed III. also had a daughter named Fahriye, but her mother was not Safiye and she was only married twice. There's no proof their lives were half as interesting as their series' counterparts, the most notable thing about them being the involvement of Ayşe sultan, Safiye's daughter, in charity.
• In the series, Ahmed has only sister, Dilruba; in reality, he had multiple, including at least two who were daughters of Halime and another two who were daughters of Handan. Not much is known about them, besides (sometimes) what pashas they married and when. Not even their names are known from completely reliable sources. One of them was indeed married off to Kara Davud, though.
• The show significantly downplays Handan's power in the first few years of Ahmed's reign. In fact, it was her, not Kösem, who helped him to get rid of Safiye's supporters in the divan. Conversely, Kösem's power during Ahmed I.'s reign is greatly exeggarated - despite being his favorite, Ahmed apparently didn't allow her to influence him that much, as he was worried he would be perceived as ruled by women, which in turn could very well remind people of his father, whose influential mother Safiye was extremely unpopular.
• Speaking of which, the series also makes Haci Mustafa aga, one of the most influential harem eunuchs in Ottoman history, into little more than Kösem's sidekick. It was actually him who ruled the harem after Handan's death, not Kösem, although they were allies. There are some speculations that she learned more about Ahmed and gained more influence on him trough Haci Mustafa, since Ahmed was wary of being openly influenced by women. Either way, it was Haci Mustafa, not Kösem, who primarily pushed for Mustafa as Ahmed's successor.
• While Handan could've been poisoned, it's just as likely she died of some illness. All we know about the cause of her death is that it could've been mistaken for an disease of digestive tract. Rumors also circulated that her state worsened after one of her pasha protegees was executed, which the show didn't depict. It also couldn't have anything to do with Derviş pasha's execution, since became a Grand Vizier only after her death.
• Several Ahmed's children, whose mother in show was Kösem, might not in fact been hers. This includes Mehmed, Gevherhan (though it's more likely Kösem actually was her mother) and Burnaz Atike. The show omits several of Ahmet’s other children, such as Suleyman, Selim, Hanzade and Abide. It's not that most of them don't play a bigger role in the series, that is quite understandable considering how many of them there were - but we don't get even a hint that they existed, where Kösem's daughters are present at least in part of the season despite not having many speaking lines or effect on the plot.
• In the show, Derviş pasha is killed because he is responsible for the death of Ahmed's father. In fact, it were his draconian tax laws and general unpopularity in the divan that became his downfall.
• Overall, Ahmed is somewhat mischaracterized by being portrayed as something of a Nice Guy, when in reality he had quite a temper and was fixated on projecting strenght. His numerous military defeats are omitted too, including a pretty ridiculous incident, in which shortly after embarking on his first campaign he got so sick the whole affair was cancelled, and a quick peace had to be made.
• Osman gets something of an Historical Hero Upgrade, with the show significantly downplaying his overall incompetence and, in a more blatant example, makes the execution of Mehmed, his own brother, a result of Safiye's plotting. His actual reason was his upcoming campaign into Polish-Lithuanian Commonwealth, during which his absence would allow for a coup in favor of Mehmed, who was close to him in age and thus a bigger threat than his other brothers, who were only children.
• We don't know when Halime died, but if there's one thing we can be sure of, it's that it definitely didn't happen the way it did in the series - poisoned by Kösem as part of her coup. In reality, after a rebellion arose against Mustafa, Halime was persuaded by state officials to give up the throne in the name of her son, in exchange for sparing his life. Mustafa and Halime both died forgotten in the Old Palace.
• Mustafa's second deposition as a whole was very different. In the series, it's orchestrated solely by Kösem; in reality, while she might have been involved behind the scenes, we have no way of proving this, as the actual event was a response to so-called Abaza Rebellion (whose leader was the eponymous pasha Abaza Mehmed).