Ending Fatigue: Many players rarely make it to 1936, usually ending their games around 1910 or so. Part of this is that the game mechanics, though great for simulating the first 80 or so years of the game, start becoming less believable once the 1920s and 1930s roll around.
The game also begins to suffer serious slowdown on most PC's to thanks to the absurd numbers of pops it has to keep track of which doesn't help.
Game Breaker: While the two principal German nations Prussia and Austria are by themselves no means weak when either one of them meets the right conditions they can form Germany and if one controls all German territory then they can form Greater Germany. The bonuses and advantages of Greater Germany are so numerous that they can basically overwhelm and easily beat even the other great powers of the game.
Westernized China has Memetic Mutation status as Game Breaker. 1/5 of whole population at the game start is under China's control and in final years of game it's still about 1/6. Good resource base. Mostly pathetically weak neighbours. We Have Reserves after the military starts to use modern equipment turns every single war into series of Curb-Stomp Battles, where Chinese will simply overwhelm their enemies with absurdly large armies without much effort. If everything goes smooth, China can westernise as fast as late 1860's (the game starts in 1836), giving you plenty time to heavily industrialise, research the most vital technologies and easily participate in Scramble for Africa, which can turn into painting it whole in yellow. As of new version, it's still possible to modernize quite fast through conquering, but receiving the best of all the techs that have been researched when Westernizing no longer happens.
The United States can become this with a decent player, since it's the only Great Power that starts with extensive political freedoms, has a decent military and industrial base, and the weak and backwards Mexico from which to pick territory off of. With enough preparation, you can seize Canada from the UK and can gain cores on Cuba through a decision. After this and the end of the Civil War, there's really nothing stopping you from sweeping through the Americas unopposed since any nation that can challenge the US militarily is an ocean away and the Latin American nations can easily be curb stomped.
Genius Bonus: With the abstraction of sliders, and knowing that your pops act perfectly rationally, you can actually see how supply-side or Keynesian economics work - surprisingly well. Try it out! An economics graduate who masters the UI will have an economy humming along in no time.
Inferred Holocaust: Once you've colonized an area, usually in Africa, the speed at which the native population is replaced by yours (it can be up to 99% European in as few as five years) is a little alarming.
The ethnic ratio was fixed and colonial POPs are impossible to assimilate now. Players first must turn colonies into states, which gives local population equal rights with the metropoly. Since it's extremely hard by the Darkest Africa expansion, it hardly ever happens.
Stupid Evil: Out of the ideologies that seek to impose some form of dictatorship, The Anarcho-Liberals tend to be the least practical, especially if your playing as a less industrialized country short on capitalists since their economic policies will seriously hinder industrialization. If you wish to attract immigrants, their reversal of political reforms and establishment of a dictatorship will also hinder immigrant attraction.