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.
Anvilicious: Surprisingly averted for the most part. While there are a good deal of filibusters and author tracts in-verse (even from the narrator), they come from different perspectives, all not necessarily treated as better than others. Yang himself lampshades this by pointing out contradictions and hypocrisies in his own beliefs. Those said, there are times when Some Anvils Need to Be Dropped.
Prince Braunschweig, heir of the Goldenbaum dynasty. Braunschweig acts swiftly to crush any hint of rebellion from any subordinate and shows no remorse at all at any deaths that occur. He continues the Goldenbaum dynasty's despicable policies of eugenics and oppress to the populace, but his crowning achievement of villainy is when protests against the Goldenbaums occur at the colony world of Westerland. Braunschweig simply decides to kill every inhabitant on the world with a nuclear strike. Ironically this has the opposite effect he intended and simply makes the Anti-Hero Reinhard's campaign against him more popular.
There is also the first Emperor of the Galactic Empire, Rudolf von Goldenbaum, who slaughtered billions of people with his Eugenics Policies. The handicapped, gay, mentally retarded or ill, or poor were killed. Though, due to how big of a population there was in the Empire, hardly anyone noticed the billions of deaths until after the effect. Those who noticed were understandably reluctant to speak out, as all suspected political dissidents were persecuted even worse, often being summarily executed in public places in broad daylight. The day karma came calling, Rudolf only cemented his status: when his only son, borne to him by his favorite mistress (and possible One True Love), was discovered to be a congenital idiot (simultaneously invalidating all his übermensch rhetoric and kicking him in the balls on a personal level), he ordered that any and all involved in the birth be executed - doctors, nurses, even the mother herself. Living to old age with no loved ones and Dying Alone hardly seems punishment enough, but like Real Life, life in Legend of the Galactic Heroes is seldom fair.
Ensemble Darkhorse: You would expect that either Reinhard or Yang Wenli would be the most popular characters of the show. Granted, they are popular, but who is the absolute darling of ficwriters and discussants? The enigmatic, electronic-eyed and utterly ruthless Paul von Oberstein.
Foe Yay Shipping: How some fans interpret the relationship between Reinhard and Yang.
Genius Bonus: In episode 39, Yang explains his view on the political situation between the Alliance, the Empire, and Fezzan to Julian. Anyone with a background in political science (especially in international relations) will recognize his explanation as a simplified version of the Realist school of though, especially the Balance of Power theory.
Harsher in Hindsight: There's a moment as early as episode 17 where a character mentions to another that if he's in trouble, "I'll get you to come save me". And then, around sixty episodes later, Yang is shot and dies, with Julian arriving minutes too late.
Yang died within a single year after marrying Frederica, and during which they spent less then three months living in peace together. Considering how things turned out in the end, his inner monolog after proposing to her about how he didn't peruse her romantically before this point because he doesn't deserve family happiness becomes tragically accurate.
Heartwarming + Hilarious in Hindsight: Episode 13 has Kesler having to deal with Reinhard's "scorched earth" tactic on a planet, while dealing with a woman named Vier, whom he would have did Childhood Friend Romance with, but left to join the military, and when he sees her again, he hears she was married and has a son, but find out her husband died in combat, and the kicker, Vier is voiced by Sakiko Tamagawa, who is currently the wife of Shuichi Ikeda (Kesler's voice actor).
Or possibly the second best, as there was someone capable of easily manipulating him. His identity? Emperor Friedrich IV. Who knew perfectly what Reinhard was planning, and made sure he had the means to succeed (and even covertly teased him about his ambitions), without Reinhard noticing. And it's strongly implied that he wanted Reinhard to take the throne and reinvigorate the Empire, knowing fully well that the Goldenbaum Dynasty's days were numbered.
Louis Mashengo. Yang Wenli never remembers who he is and often wonders why he is around. When taken out of context, it carries some rather Unfortunate Implications.
Taking Oberstein's ever-stoic face and captioning in things like "rofl XD"
Moral Event Horizon: Oberstein keeps teetering on the edge, and arguably crosses it with the Westerland incident - made only worse by the fact that his actions proved to have an overall positive effect for Reinhard and his followers.
Adrian Rubinsky starts out as a ruthless schemer who only cares about profiting from the war. At the end of the show, however, he dies of a malignant brain tumor. Then we find out that his death would trigger bombs all over Heinessen, killing god knows how many people in the process. Any why? Only so he might take Kaiser Reinhard down with him. For someone who was a Magnificent Bastard for most of the show, this act of pointless destruction sure makes him seem like a monster.
Stoic Woobie: Oskar von Reuenthal. He has Mommy Issues, which are his Freudian Excuse for never being able to form a lasting relationship with his lovers, knocks up a woman who wanted to kill him, and is wrongfully accused of treason twice, the second time deciding to go along with it because he's too prideful to clear his name a second time despite knowing that he's outnumbered and will probably die. No wonder why he he's Mittermeyer's drinking buddy, who wouldn't want to buy the guy a drink (besides Oberstein and Lang)?
There are a couple of jokes about Frederica's cooking ability that given that she's both a naval officer and later, a politician would seem a little out of place in a modern, western show.
While Frederica may hold a relatively low official rank, the unofficial power she commands is rather substantial. As both Yang's wife and his adjutant, Frederica is basically his closest and most important advisor, and inherits his full political power following his death. It also seems likely that, with the end of the war and the new peace, that she will continue to hold a prominent role in Heinessen/Imperial politics.
A greater source of dissonance, at least from the point of view of modern liberal democracies, is the willingness to admit that autocracy can be preferable to democracy under certain circumstances. In the end, the Autocracy dominates the entire inhabited galaxy (with Heinessen left as a Democracy reservation), though there are hints that it will become a Constitutional Monarchy through gradual reforms.
At some point, the narrator made the statement that the Alliances' democratic decay and eventual downfall was the result of them having an open door immigration policy, allowing immigrates that that don't share their social values to eventually erode away their republican principles while weakening their social structure. This has some very Unfortunate Implications, considering how similar this is to the rhetoric by some of the far-right political parties concerning immigration policy in their own countries.