These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
YMMV: Hearts of Iron
Evil Versus Evil: Depending on the course of history, it's entirely possible for the game to end in a final showdown between an alliance of fascist dictatorships and their conquered puppet states and an alliance of equally repressive Stalinist dictatorships and their puppet states.
Game Breaker: The United States is pretty much considered "easy mode," and for good reason, particularly in III. They start off with the largest amount of IC in the game, the biggest knowledge pool, and a very powerful navy - and it only gets bigger and meaner as the game progresses. Ironically, this is toned back compared with how powerful the US economy was in World War II. The only weaknesses the US has is that starting out, they have a weak army and air force and low technology, so using that knowledge pool is essential to catch up with the rest of the world. But by '45, the US will almost always be in a dominant position, as the only other economic powerhouse, the USSR, will have almost certainly spent a lot of resources and taken a lot of damage fighting Germany. Later expansions make them even more broken, with For The Motherland actually allowing the US to get a massive manpower boost once "The Day of Infamy" event triggers, which not only adds 400+ manpower instantly to their pool, but also revokes The New Deal (which imposed a manpower penalty on the USA) and gives a 25% bonus to manpower growth for a couple of years.
In III, using wars with minor countries to let you pass Total Economic Mobilization and Service By Requirement laws lets you swell your IC and manpower by a hilarious degree before World War II starts. Especially bad if you're a major power, and just ignore the "war" while you build up a huge number of divisions, planes, and ships. This got so bad that for the Their Finest Hour expansion, a special restriction was set where those laws could only be passed if the enemy you faced had a minimum of half your IC, otherwise you're stuck with just War Economy and Three-Year-Draft.
Earlier editions of III turned your intelligence apparatus into one of these when used properly. The "Sabotage Production" mission, when coupled with "Counterintelligence" to eliminate enemy domestic spies, enabled allowed you to utterly cripple an enemy's industrial capacity, to the point that, for example, Germany would take months to conquer Poland and would get stonewalled in France, leaving them ripe for an American or Soviet attack. Later expansions removed the ability to sabotage production.
Good Bad Bugs: A recent DH patch had instances where after the Soviet Union lost a war against the axis and accepting the bitter peace event, Lenin would take over as Head of State of the Soviet Union, cue jokes about Zombie Lenin coming back to Set right what once went wrong