The usage of the term "Norman" is a huge Anachronism Stew, as it comes from the 10th century. Norman chiefs being units from the Britannian civilization in the third game is strange as well, as Normandy is a northern region of France that had little interaction with Britain at the time (ironically, the first and second games get this right by having them in the Gaul civilization).
In the third game, Britannian druid Penut chants the name of Kathobodua, a continental Gaulish goddess who has never been mentioned in the comparatively richer Britannian religious sources. This is presumably an in-game reference to the goddess's role in the first game, though.
Fand is an Irish deity, not a Gaul one.
"Catriona" is a Britannian form of the Greek name Catherine. In the game's setting, it would have been impossible to find an Iberian person with that name.
The Iberian faction in the game is actually a rather outlandish mishmash of cultures from the Iberian peninsule, including, but not limited to, southern Iberian Greco-Phoenician art style, northern Celtiberian architecture, and some Celtic-looking warrior units.
In real life, Hispania was pretty obscure in the religious aspect. Northern tribes apparently had shaman-like "diviners" who were entasked with sacrifices, while southern regions could have believably shared Carthage's Phoenician pantheon and priests. The game opts, however, to portray their religious class as composed by female priestesses clearly based on the dama statues of Spanish archaeology, a portrayal that has its own problems (namely, that those are actually limited to the Mediterranean coast and that we don't even known if they are meant to represent priestesses, goddesses or noblewomen).
In real life, Carthage's religion was carried on by priests that were clean shaven for ceremonial reasons, not bearded "shamans" like their counterparts from the game. Also, some of their in-game quotes mention Moloch, which was actually a posterior and vaguely pejorative Hebrew word for any Phoenician god; a person from Carthage would have referred to his god as Baal Hammon or simply Baal.
The origin and timeline of Tuareg ethnic identity is a complicated matter, but one thing is sure: there were no Tuaregs in the Carthaginian army.
Gladiators were entertainers and prizefighters, not soldiers. Rome would have never sent them to the battlefield, at least not while wearing gladiator gear, which was designed for the spectacle and was quite impractical in serious warfare. Speaking about it, the game mixes up two kinds of gladiators in their portrayal: their unit wears a Murmillo helmet yet wields a Retiarious trident.
There really were foreign slaves who gained their freedom and became soldiers and officers in the Roman army, just like the game's liberati, but, upon doing so, they would naturally adopt the Roman army's attire and weapons. In the game, they are portrayed as barbarian-looking guys wearing loincloths and wielding axes.
Tribunes were military commanders, not frontline warriors, and they definitely didn't fight while Dual Wielding gladii.
Celtic and Germanic warrior women are really recorded in history, but their portrayal in the games is certainly rooted in either Rule of Cool and/or Politically Correct History. In real life, it was frequent for women from these cultures to accompany the men to the battlefield in support roles, acting as cheerleaders and combat medics who would join the fight if the men were overpowered (or if they tried to desert, in whose case the women would attack them), but to form Amazon Brigade-style specialized units like the Gaulish warriors and Germanic huntresses from the game was much rarer, if not anecdotical.
Opposite to the previous, Spanish Celtic women are recorded as often defending their cities along with the men, but the in-game Iberians are ironically the only Celtic/Germanic faction that does not have warrior women (though Imperivm II compensates this a bit by having some Gaul warrior women among the Iberian forces in campaign, probably in reference to the mentioned records).
Celts, especially Britons and Gauls, were famous for using war chariots, but none of those civilizations has them in the game. Meanwhile Rome, who did not use them for warfare, does have them.
Gauls definitely did not have a caste of sacred warriors wielding tridents, nor used double-headed battle axes.
Germans did use battle axes and clubs, but certainly not the exaggerated giant halberds and spiked maces they wield in the game. Also, they rarely used helmets, most of the time being only the leaders who wore them, while their in-game civilization has an impressive variety of helmets and headgear.
Just like their civilization altogether, the games's Iberian army combines Mediterranean coastal elements (falcatas, oblong shields, ornated helmets) with Celtiberian ones (white tunics, oval shields, crested helmets), along with Cantabrian (battle axes), Lusitanians (caetras, leather caps, guerrilla fighters) and downright fantastical (the Blade on a Stick weapon wielded by the guerrilla fighters). Also, all the cultures from Hispania favored javelins over bows, so it would make more sense for them to have a javelin caster unit than an archer one.
Related to the previous, though so pervasive in media that it could be its own trope in the vein of Every Japanese Sword Is a Katana, the usage of falcatas by Viriathus and the Iberian faction in the game is inaccurate. As said above, the falcata was limited to the Mediterranean coast of Iberia and was rare to find on the rest of the peninsula, where straight swords were much more popular. While Viriathus and the rest of the Lusitanian elite might have probably owned falcatas thanks to trading and plundering of the southern territories, they probably didn't use them as their primary weapon.
Carthage's portrayal in the games is spectacularly wrong. For starters, it lacks cavalry, which is a huge departure from history, where they were known and feared by their varied contingents of horsemen. Secondly, real Numidians were known for being the biggest part of this cavalry, not for being infantry as Imperivm shows. Next, historical Libian mercenaries working for Carthage were heavy infantry, not unarmored javelin throwers as portrayed in the games. Also, the presence of unarmored Mauritanian guys Dual Wielding sabers is similarly fantastic, as it would be in any real culture of the time. Finally, there's no record of Carthage using Tuaregs or dromedary cavalry on the battlefield.
Carthage's Sacred Band was actually composed by spearmen in the phalanx style, not swordmen as portrayed here (they did carry swords, but just as a secondary weapon). Also, its presence in the game's events is highly anachronistic: while Carthaginian armies always featured commanders and small forces recruited among Punic citizens, the real Sacred Band was disbanded sixty years before the very First Punic War and its unit name was never used again.
In the game, Carthage's specialty as a faction is playing a Galactic Empire-style human wave strategy, with some units even being explicitly designed to inflict damage by dying. While the developers might have got this idea from Carthage's usage of mercenaries over citizen troops, which would admittedly be easier to sacrifice in battle than your own people, this is practically the opposite to how Carthaginians waged war (there's a reason why Hannibal is called the "Father of Strategy" and not the "Father of Zerg Rush") and not a very realistic military policy in any case: what sane mercenary would sign up with a nation that had the reputation to send entire armies to their deaths? This strategy would make sense if employed by Gauls, as they really loved the good ol' frontal charge and considered honorable a stupid death, but not by Carthage.
Most of the Egyptian civilization's named warrior classes (Horus warrior, Anubis warriors, Nile guards) are fictitious, as well as the first two's weapons and armor. Also, some of their warriors are barefoot, which is inaccurate, as warfare was one of the few fields where they always wore sandals.
The first game has a scenario set in 132 BC, in which the very first words of the description claim that Augustus Caesar currently has a firm hold on Rome as the first Emperor. This is off by more than a hundred years: Julius Caesar (let alone his adoptive son Augustus) hadn't even been born yet. This is not hard to notice if you're aware of the widely known fact that Julius Caesar was assassinated in 44 BC.
While it can be forgiven if we interpret that the entire Imperivm II tutorial level is meant to be fantasy, it still contains a piece of history where Viriathus was somehow a Celtiberian (there are some fringe theories about it, but historians are unanimous he was a Lusitanian), an apprentice to Caraunius (who in real life was probably younger than Viriathus), a Gaul druid named Haaser, and eventually the chieftain of Lutia (a city that was never allied to either Viriathus or the Celtiberian resistance). He is even given the unit skin of Larax from the first game, who is clearly Gaul in appearance. For extra bizarreness, there is a patch of desert and a Carthaginian settlement in the same map, and the English version of the game turns it Up to Eleven by changing the locations to the Gaul village of Kebatha and a fictitious city named Barezia.
The Romans from II apparently invented Time Travel, because their Senate in 264 BC somehow features Cato the Elder (234-149) and Cicero (106-43 BC). The former even says his classic quote "Carthage must be destroyed!" despite the fact that the real reason that led him to utter it in real life (namely, that Carthage hadn't been completely destroyed by Rome and was slowly rebuilding its power) didn't even exist at the time (as Rome and Carthage hadn't clashed yet and the latter was already a Mediterranean superpower).
At the campaign in Zama, Scipio Africanus is portrayed as an old gentleman with a Bald of Awesome (recycling the character picture of Canon Foreigner Senator Anteros from the second game). In real life, Scipio was actually a young man when he fought in that battle.
Numidians and Mauritanians were olive-skinned people, while the game portrays them as being black and having some Sub-Saharan African imagery. This is strange, as they did get the right skin tone for the Libyan lancers, even if they still got their gear and weapons wrong. It extends to the hero units too, as the game's tendency to assign them random names and character pictures messes up things: chances are that, after recruiting a Carthaginian hero, you will end up with a guy sporting a Phoenician name and a character pic that represents an Angry Black Man.
Imperivm III follows the pop culture trend of portraying Boudica as an Action Girl, but no source ever mentions her having personal involvement with her battles. The game also avoids mentioning her husband Prasutagus and their daughters, instead making it look like Boudica had always been the sole governor of the Iceni.
Events and battles
In the first game, the Battle of Gergovia is portrayed as a massive, Napoleonic-style open field battle in a plain. This was fortunately corrected in the third game, where it is accurately portrayed as a montainous assault, as it was in real life.
In Imperivm II, Numantia is placed in midst of a plain field, when the reason of its legendary resistance in real life was precisely its emplacement in a mountainous terrain with natural defenses. Again, the third game corrected it.
The second game has the Senate receiving the news about Sicily and deciding to send Appius Claudius Caudex to intervene against Carthage, thus giving the impression that they were the masterminds of the move. In real life, most of the Senate was actually opposed to the intervention, and it was Appius himself who forced them to allow it by appealing to the citizens.
Gades was a coastal city on a narrow slice of land, not a fortified city deep into the land as it was portrayed in II. Also, in the game, Gades is an Iberian city the player has to conquer, while in real life it was a Phoenician colony just like Carthage, which also means the city was allied to Hamilcar and Hasdrubal the Fair from the beginning.
Following the previous point, II gives the impression that Hispania was a completely unexplored, savage land until Hamilcar's arrival, as well as that Romans only came to the peninsula chasing the Barcids. In reality, Carthage had been trading formally with the Spanish tribes long before Hamilcar decided to take their territories by force, which is why he already knew exactly where and who he would attack to make a few good conquests (unlike the game, in which he's pretty on the dark about it until he captures Gades). Similarly, Rome had its own field of influence on Hispania before the Second Punic War, and it was precisely because Hannibal attacked it that the war exploded.
Although the game doesn't mention it by name, the Roman mission in Germany from Imperivm III is clearly meant to be the Battle of Teutoburgo, where Varus was defeated by Arminius. However, the real battle was not a random ambush to a Roman force trying to reach a city ruled by Varus as it is portrayed in the game, but almost the complete opposite: in real life, Varus commanded the Roman force personally and was attracted out of his camp through deception by Arminius, who then ambushed and killed him.
Viriathus' headquarters are located in Mons Herminius in his campaign, probably because it was, for a long time, believed to be his place of birth. However, this theory was already disproven as mere folklore by the time the game was produced. As we don't know Viriathus' birthplace, it would have been more accurate to locate his fortress in Mons Veneris, which sources name many times as his main stronghold.