Isabella the Catholic was 10 when she was taken to the Court, but in the series she's still played by then 25 years old Michelle Jenner, who looks 14 in the first scene at the very least.
20 years-old Víctor Elías plays the Infante Alfonso, who would be 8 at the beginning of the series, making him more as a cocky, unfitted teenager than the clueless kid he would have been at the time of the Farce of Avila.
On the other hand, 36 year-old Rodolfo Sancho's Fernando of Aragon very much stands out, being 11 years older than Jenner, even though the fact that the two have the same age is an important plot point.
Diego Pacheco surrenders after Fernando's victory in Zamora and breaks down crying when he is threatened with execution. In real life he had to be subdued a second time when the Portuguese invaded Extremadura, then served in Granada where he lost an arm in combat.
Boabdil is depicted as being barely able to hold a sword. In real life he was actually a great swordsman, but a General Failure.
The Granadans' style of dressing is closer to Ottoman, if not full-fledged "Arabian Nights" Days, than properly Nasrid. Granadan soldiers are also almost all armed with scimitars, when they used straight swords in real life. Finally, in a phenomenon that would need its own trope for how often it happens, the Berber Gomeres from Northern Morocco are portrayed by black actors instead of, well, Berbers.
Although he was not the heir of his family, meaning his position in the court was relatively low, the real Gonzalo Fernández de Córdoba still came from an aristocratic family and was in fact a relative to Fernando himself. Nothing of this is mentioned in the series, possibly to make his Ship Tease with Isabel feel more like the impossible love between a high queen and a lowly soldier. Also, Fernando's beef with Gonzalo after Isabel's death is either cut or happens offscreen.
Tomás de Torquemada is characteristically portrayed as more of a bloodthirsty loon than he was by all accounts.
Christopher Columbus' characterization, which makes him arrogant, uncultured, a con man and a liar, also reflects more classical pop culture preconceptions about him than what we know for sure about his personality. It's also notable that in the series, Columbus is helped in the intellectual tasks of his projects by Moor sages rather than Franciscan monks (consultants like Juan Pérez and Antonio de Marchena are fully excised, and it's not even mentioned that the Franciscans were who put him in contact with the crown in the first place), making it look like the merit of his enterprise was more due to Muslim brainpower than their own devices. This caused a bout of controversy in real life, with Andalusian politician Elena Tobar criticizing the series for the deviation.
Carlos, Rey Emperador
Being a Habsburg, whose mother tongue was German, Charles V didn't speak Spanish when he arrived in Spain, though he learned it real quick. Emperor Moctezuma also never learned Spanish at all. The series skips both language barriers, presumably for the viewer's sake.
In the series, William de Croÿ burns Cardinal Cisneros' testament, which never happened in real life. In fact, the testament is currently in the national archive in Alcalá de Henares.
Actor Álvaro Cervantes is infinitely more attractive than Charles V was. Also, he doesn't have a noteworthy jaw like Charles had (granted, this would have been hard to achieve without prosthetics — chroniclers of Charles's own time already described him as looking like he was wearing a big fake jaw).
The real Francis I was not as knockout-handsome as his actor Alfonso Bassave, and he apparently had also a long nose and a funny voice.
Although Hernán Cortés was not unattractive in real life, his actor José Luis García Pérez is much more of a Hunk than Cortés was.
Mary Tudor is described in-universe as being old and unappealing, and tradition has certainly that she was so by the point Philip married her. In contrast, her actress Ángela Cremonte is nothing short of beautiful and doesn't look old at all in her character.
The worst case, however, might be Claude of France, whose actress Eva Rufo is elegantly attractive despite Claude was reportedly very ugly in real life.
A strange inversion happens with Philip II, who was a handsome dude in his youth, yet is played by Marcel Borrás, who is more of an average kind of guy and also sports unflattering haircuts as part of his character. As a result of this point and the point above, in this series the English royal pairing is more of a case of Ugly Guy, Hot Wife when in real life it was one of Hot Guy, Ugly Wife.
In real life, Francis I was only six years younger than Charles of Bourbon. In the series, although their respective actors are only eleven years apart, not much more, it happens that Alberto San Juan (Charles) looks way older than Alfonso Bassave (Francisco), with an almost fully white beard to boot, to the point the two noblemen could pass rather as father and son.
Moctezuma's actor Cristhian Esquivel was also below 40 at the time and arguably looks quite youthful for his age, while Moctezuma was 54 at the time. Cuauhtémoc's actor Nelson Dante looks the same age as him, if not older, when in real life Cuahtémoc was almost thirty years younger than Moctezuma.
In a goof which sparked a lot of controversy, Charles is shown swearing the crown of Castile with the formula used in the crown of Aragon.
The series shows Jakob Fugger originally backing Francis I's candidacy before switching to support Margaret and Charles under promises of Aztec gold. In real life, this never happened; Fugger already had a long history working with the Habsburg family and had backed Maximilian I before his death, and not securing Charles on the imperial throne would have meant a terrible loss of inverted money for him (which he went to recover after Charles was chosen).
In the series, Fugger secretly bribes Franz von Sickingen and arranges for him to assault the election's building and force the council to choose Charles at sword-point. In real life, it was Charles himself who allied with Sickingen and his Suabian League, and publicly so. Sickingen and the Suabians did pressure the electors with military force, but not to the extent of raiding the very election.
The series portrays the Italian Wars as less of an one-sided affair that they were in real life, at one point implying that the Battle of Bicocca was the only victory Charles had achieved against France in the Four Years' War before Pavia. In real life, Francis was losing that war badly and Pavia only finished it.
Charles of Bourbon's betrayal happened much earlier into the Four Years' War and was not instrumental for Charles V's victory, and he did not seal the Battle of Pavia by suddenly changing sides with 30,000 men at the last moment. In reality, he betrayed Francis only a year into the war, participating in a plan with Charles and Henry VIII to divide France among them, but he was discovered and forced to flee, not with 30,000 French soldiers but almost alone (him retaining so many loyal soldiers is somewhat of a Plot Hole in the series given that Francis had confiscated all of his titles and money). He was welcomed as an imperial commander and took part in a couple battles more against France, and later arrived in Pavia as part of the army of imperial viceroy Charles of Lannoy. The scene where he fakes illness did happen in real life, but it happened after he had already secretly betrayed Francis and not while he is pondering about it as in the series.
In the series' rendition of the Battle of Pavia, the battle starts by day, while in real life it started as a night raid. Also, King Francis is found and captured in a barn, when in real life he got captured in the battlefield when his horse was killed under him.
The series' portrayal of the Spanish Conquest of the Aztec Empire is very, very loosely based on real life, to the point it only follows it in very general terms.
The subplot of Cortés and the explorers protesting against Chievres giving their jobs to Flemish noblemen is entirely fictional. Contrary to what the series and many people seem to believe, Cortés was never considered a rebel in the empire, and in fact gained King Charles's seal of approval quickly after his controversial breakup from Governor Velázquez, while in the series Charles never gives him such, and instead treats him as if he was the devil incarnate until way after New Spain is conquered.
The character of Juan Velázquez de León, who in real life was very minor and died before the Siege of Tenochtitlan, is a Composite Character with several of Cortés' lieutenants, such as Pedro de Alvarado (for being the highest ranked and closest to Cortés, as well as the one being later given license for sea exploration) and Cristóbal de Olid (for having been Governor Velázquez's servant, and a future traitor to Cortés). Also, as the Tlaxcaltecs don't seem to exist in this continuity, he never marries an indigenous princess. Moreover, the real Velázquez was a stutterer, while this version of him isn't.
Cortés finds Gerónimo de Aguilar entirely by chance outside of his camp. In real life, Cortés was already informed about him and sent people to his village in order to recruit him. This version of Aguilar is still dressed as a churchman and looks a bit shell-shocked from his years there, while the real deal had adapted rather happily and was wearing native garments to the point he looked like one of them.
The previous scene introduces La Malinche in spectacular fashion by pulling a knife on Cortés, which would have been utterly out of character for what we now about her personality and intelligence. It also reveals that Malinche is her indigenous name (presumably Malintzin), which in real life is Dated History; it is believed to be rather the indigenous form of her Christian name, Marina.
The Totonacs are conflated with the Tabasco Mayans, and they don't look particularly unhappy under Mexica rule.
As it could not be otherwise in pop culture, Cortés and his men wear the ubiquitous morrión helm, which in real life wasn't used until half a century later, and leather kneeboots, instead of the alpargates more proper for hot climates. Marina and the indigenous women also wear fantastic Fur Bikini-like attires that have nothing to do with the long hupil robes they would have worn in real life.
As it is usual in portrayals of the Conquest of America, Cortés and his men are here almost alone in their war against the natives, instead of being at the head of a massive army of Tlaxcaltecs and other native states that allied with them against the Mexica. Only in the scenes mentioned above, Cortés' men should have been accompanied by a Tlaxcaltec guard almost twice their own number, who in real life would be instrumental for Cortés and company to get out of the city alive. In the series, there is only a throwaway line by Malinche that Cortés will need the help of the Mexica's enemies, but this doesn't happen onscreen, other than some Totonacs following Cortés' expedition to Tenochtitlan (which, amusingly enough, they refused to do in real life because they believed it to be a suicide mission).
We don't get to see much of the Mexica Empire, but it's notable that every Mexica appeared onscreen is displeased by the ways of Cortés and company, while all of the nastiest aspects of their cultures, like cannibalism, imperialism and Human Sacrifice, either happen offscreen or aren't mentioned at all. Moctezuma actually berates Cortés because the Alvarado Massacre ended with many butchered Mexicas, an especially funny claim considering that the Aztec religion involved constant sacrifice of imperial subjects. The very festival interrupted by the massacre included human sacrifices, despite Moctezuma claims "it was only a party".
It's already notable that the Alvarado Massacre happens without Alvarado, who in this series is Adapted Out, but even more than all of the massacre seems to happen in mere seconds while Cortés and Malinche are getting love-dovey in a hammock. In real life, it happened while (and because) Cortés was away warring against a rival conquistador, Pánfilo de Narváez, who had been sent by Velázquez to capture him. The massacre of the series, which receives no justification (in real life, Alvarado apparently believed the festival was actually a trap to kill them), also has the Spaniards randomly going to sack the royal treasure, after which Moctezuma is murdered by his courtiers in his throne room, nothing of which happened in real life.
The Sad Night is entirely skipped, as Cortés and company are seen successfully fleeing from the city by night, or at least happens offscreen and is never mentioned.
In the series, due to Malinche's manipulations undermining his sanity, Cortés screams to Catalina that he is the god in the New World (no, not that way, but almost). The real Cortés was extremely Catholic even by his time's standards and would have likely never been so casually blasphemous.
Catalina's threat of destroying Cortés' career by denouncing his infidelity is treated as Serious Business, with Cortés strangling her to death to impede it, but this would have not been the case. While it's true that Cortés had an exceptionally bitter marriage with her and all the evidence implies he did murder her, male infidelity was hardly a rarity in the setting and would not have given him much trouble in the court (in fact, the real Cortés was a known womanizer, with multiple legitimized bastards, yet this was never much of a political impediment for him).
Contrary to what Carlos shows, Cortés and Francisco Pizarro were not cousins, but nephew and uncle respectively, and they were distant enough that it's believed they didn't know each other personally, rather than being close comrades as in the series.
The incident where Cortés unsheaths his sword for King Charles to kill him with it seems to be inspired by a real event where another conquistador, Miguel Díaz, did it on Cortés himself. The rest of the meeting, even if more faithful to history, is just as histrionic, as in real life Cortés was never arrested and there's no evidence that the king was so disdainful on him right on his face.
In real life, Cuauhtémoc was not imprisoned up to his death, and in fact was given back the throne of Tenochtitlan and continued ruling in the king's name. Cortés executed him while they were both part of an expedition to the Mayan lands, where hunger and perils drove the Mexica auxiliars to consider revolting, but in the series, as the expedition never happens, Cortés executes him in the Mexica Empire and for an unspecified act of treason to eliminate an untrustworthy chieftain before starting his sea exploration travels. Cuauhtémoc's line accusing Cortés of having many deaths on his conscience, coming from the huey tlatoani of the bloodthirsty and iron-handed Mexica Empire, is definitely ironic.
The series doesn't mention that Antonio de Mendoza y Pacheco was María Pacheco's brother, which may imply they aren't related in this continuity. In any case, Mendoza is portrayed quite negatively, being smug and smarmy, and even directly conspiring against Cortés, but there is no evidence this ever happened in real life.
The subplot with Bartolomé de las Casas and the abuse of the encomienda system follows real history, but the level and kind of abuses portrayed are misplaced and unrealistic for New Spain, where large indigenous states were still intact and turned into vassal realms to Spain, so inflicting large scale abuses of the kind described would be difficult to pull and would have provoked entire wars.
Racist lines are thrown in here and there, even although otherwise intermarrying happens onscreen. Mendoza even claims that blacks are subhuman, when in real life there had already been plenty of black and mulatto conquistadors, including some examples in Cortés' own entourage whom Mendoza himself would have probably treated personally. Paul III's bull declaring the indigenous' humanity is real, but in real life it was mostly a formality by this point — Queen Isabella herself had ruled in favor of the indigenous as human beings as soon as they were discovered forty years earlier.
De las Casas did really propose to replace Indian labour with black slaves before realizing his mistake, but unlike what the series shows, importing black slaves to America was not his idea and was already happening in the Spanish Empire, or rather in any empire or country that could afford it at the time.
Before the Valladolid Debate, Borja claims to De las Casas that most masters of the School of Salamanca are sympathetic to Juan Ginés de Sepúlveda to the point that his victory is ensured, when in reality many of them were protegees of the late Francisco de Vitoria, who had similar views to those of De las Casas. There is some popular perception that De las Casas was the underdog coming to the debate, which is inaccurate in any case, as his stance on the natives' protection was hardly new and had been popular at least since Vitoria's times.
The series does note accurately that De las Casas's report on native abuse is an exaggeration that will surely be weaponized against Spain, but it leaves it ultimately hanging how much it actually exaggerates. In real life, research has proposed that most of what he tells is made up, which truly fantastical numbers and supposed crimes.
Carlos adapts out Emmanuel Philibert of Savoy and puts the Duke of Alba in his place during the Battle of St. Quentin. In real life, Alba was busy guarding Italy from a French invasion, the latter of which is mentioned in the series as a menace to deal with immediately after the battle.
in real life. Finally, in a phenomenon that would need its own trope for how often it happens, the Berber Gomeres from Northern Morocco are portrayed by black actors instead of, well, Berbers.