Contested Sequel: The fandom is really divided on whether EU II or III is the superior game (though III has won more supporters with each Expansion Pack).
And again with EUIV, the fanbase is divided on whether it's truly a better game or just EUIII with better graphics.
Broken Base: Comes with practically every update to EUIV, with some saying that Paradox is destroying the fun of the game in attempts to nerf exploits, while others say that the changes are necessary to stop the game from being too easy. On the other hand, numerous changes are made to reduce player agency to minimum and thus giving AI a fighting chance... instead of improving AI.
The biggest and most divisive issue for IV was probably introduction of colonial nations. The moment player colonise specific amount of provinces in arbitrary decided regions in Americas, Australia and New Zealand, a colonial nation is automatically formed from the colonies and from then on works as a vassal, while each new colony in that particular region will be automatically handled over to the CNs. This is all done with absolutely zero control on player side. For some players it is enough reason to not colonise at all, treating them as money sink with zero monetary gain, while others love the fact CNs build large armies the mother country doesn't have to pay for and then provide them as expeditionary forces whenever asked. Bringing this issue on Paradox forum is almost guaranteed way to start all-out brawl.
Demonic Spiders: The Divine Wind expansion pack turns the Golden Horde and Timurids into these for everyone between Eastern Europe and China.
Firearms against low-tech enemies, especially in II. Combat is divided into two phases: fire and shock. Before you gain fire value for any of unit types, fire phase is skipped for your armies. Fire phase by default mostly affects morale. So for half the combat low-tech armies are doing nothing, while getting their morale wrecked.
Artillery in all parts, especially early on. It can turn sieges into relatively short affairs, since the scaling of artillery-to-fort ratio is pretty low at this point and it will take AI quite a while to fortify adequately all provinces. And that's assuming AI has tech to improve forts in the first place. Starting from III, artillery can double your combat power, as it gets positioned in the second row of fighting armies. Since AI can't really compose proper armies nor utilise artillery at full efficiency, it can quickly turn wars into series of curb-stomp battles. Especially since artillery is not affected by culture group and everyone gets the same guns with tech progression.
Inland trade nodes in IV. Trade nodes with access of sea can be affected by and with privateers and general use of ships to gain control over the market. With proper tactics and national ideas, it's possible to control more trade with fleet than by directly controlling provinces within the node, especially if numerous nations compete each other. Inland trade nodes draw entire control power from the provinces within the node, so controlling all of them provides a nation with monopoly that can't be affected by anything by outsiders. This of course provides considerable profits with almost zero investment in trade power. Special mention goes to Kraków and Xi'an trade nodes, which are at the game start almost fully controlled respectively by Poland and Ming and nothing short from extensive conquest can change that.
If outsider nation sends its merchant anyway, they will gain a small fraction of control, but it's negligably low and AI will rarely try doing this, having already limited resources.
Good Bad Bugs: The AI does not understand the concept of attrition. It's entirely possible to lure a large army into your territory, Scorch the Earth in that province with a fast / sacrificial unit, and let that (or the winter) whittle the enemy army down to almost nothing.
The flipside is that naval attrition has to be disabled for the AI, leading to things like Ottoman territories in the Baltic, or Castille owning Finland.
Naval attrition in European waters is nigh-nonexistent anyway.
If the player starts the game anytime later then 1399, the game would remember all changes that happened since that year and mention them in the country's history log. Start the game as the USA anytime after 1797 and read how George Washington's period was only remembered for his drunkenness!
Memetic Mutation: On the forums, someone started a thread titled "Can Poland into space?", which is itself derived from Polandball. This has become a minor meme, with the Strange Screenshots thread containing many instances of nations claimed to "into space" - apparently it's the new word for "blobbing". The backlash is summed up by this image◊.
Ascended Meme: As of Divine Wind, "Poland can into space" is an achievement acquired by reaching maximum level in all technologies as Poland.
Also, "Spain is not the Emperor." It appears on the loading screen as a hint. And it was followed up with the achievement "Spain is the Emperor."
From Europa Univeralis 4: "You can never have too much grain". Cue threads and threads devoted to the awesomeness of grain and grain-inducing puns.
The reddit sub r/ulmgonewild is dedicated to the adventures and shenanigans of the greatest German city state to have ever existed.
"Steppe Wolfe" - common on the Something Awful Forums when describing a game that's gone horribly glitchy, ahistorical, or involving Bulgarians. It's a reference to a So Bad, It's Good mod which had, among other things, a bug in which during the fall of the Soviet Union the country of Estonia somehow manages to secede from every single country in the world simultaneously and go to war with all of them. It's also one of the few mods where you could get this message (paraphrased): "My lord, news from the country of the Soviet Union: They have thrown off the shackles of their former master Quebec and are experiencing freedom for the first time in ages!"
Most Annoying Sound: The sound effect that plays whenever there is a rebellion in your country. You will come to loathe it if you try to establish a wide empire by conquest.
Scrappy Mechanic: While the fandom is extremely divisive about Europa Universalis IV, at least one thing can be agreed upon - mana system is just badly implemented. Or rather not mana itself, but the way it is gathered. To perform pretty much any action in the game, you require specific amount of administration/diplomatic/military points, with growth based on skills of your ruler - which are randomly generated and you have zero influence about. You can increase the skill with appointing advisors, but they cost a lot over time and you also have zero influence on how good they are or what bonus they will grant, often hiring absolutely useless people for loads of money just to mitingate the atrociously bad monarch. Republican governments in theory allow you to pick what kind of ruler you want, but they are almost always one-trick ponies. Latest expansion, Rights of Man, slightly improved the situation with certain types of governments and giving general ability to abdicate and disinherit your oldest child (saving your country from truly incompetent monarchs), but it's still about managing absolutely random outcomes and thus far from perfect. And there is nothing worse than being stuck with string of bad rulers, over which you have no influence.
It was proven long time ago life expectancy of a character depends on their skills - the better they are, the shorter they live. Which means you can end up with bad rulers lasting for well over 70 years on regular basis and completely forget about keeping all those great historical rulers alive pass their late forties, even if they often enjoyed long lives in real life. Starting as Spain under Carlos II can in fact have worse results than it happen to have in real life.