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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.
Alternatively, the equally downer view that, while opposing the "strength at all costs" elements within the government that would give birth to those ugly events, Katsumoto's high-minded ideals would ultimately be subverted by them.
One moment that can be funny with the right audience — ninjas bursting through walls. "Damn those paper walls. They can't keep anything out."
The Total War: Shogun 2 expansion pack "Fall of the Samurai" is focused around the modernization of Japan (as well as the conflict of conventional Japanese weapons against guns and cannons), with you being very capable of reenacting the movie's final battle.
I Am Not Shazam: Algren is not the last samurai, Katsumoto is. See Word of God. Or, alternately and arguably more appropriately, the last samurai are Katsumoto and his men, since the word is both singular and plural.
Moral Event Horizon: A certain massacre of a Native American village by Bagley, the raid being in response to attacks on his forces from around the region. Note that while it's clear that this event (which, while horrific, is implied to be nothing particularly notable from Bagley's point of view) causes Bagley to cross the horizon for Algren and presumably the audience, it's some way into the film before we actually learn why the latter hates the former so much.
Narm: For a movie that had pretty good fight choreography that was reasonably faithful to the martial arts involved, the way that Nathan killed Bagley was just bizarre. Nathan grabs a katana, reverses it in his hands, then throws it like a spear at his target. The throw itself - and the way the katana flies perfectly straight through the air - just looks weird, and that's not even getting into the fact that katanas are slashing weapons and are generally bad at stabbing, even when they're still in someone's hands at the time.
Protagonist Title Fallacy: The Last Samurai refers to all those who fought in the Satsuma Rebellion, not Tom Cruise. Part of the confusion is that Samurai can refer both to a single warrior and to a group, in this case it was the latter. A fact completely lost on the translators of many countries:
In Sweden, they named the movie Den siste samurajen (the explicitly singular form); the plural form would be De sista samurajerna.
In Russia, Posledniy samuray, instead of Poslednie samurai.
In Italy, L'ultimo samurai, instead of Gli ultimi samurai.
In Spain and all the Spanish-speaking American countries, El Último Samurai instead of Los Últimos Samurais.
Tear Jerker: The samurai's charge almost breaks through... but then they are coldly gunned down by the army's new Gatling guns. Already emotional enough, but then Hans Zimmer's score turns it into an incredibly gut-wrenching spectacle.
Moments later, Algren helps Katsumoto commits suicide... and as Katsumoto is dying, he sees a Cherry Blossom tree in bloom. As he sees the blossoms fall, he says: "Perfect. They are... all... perfect...". Pass the Kleenex, please.
The conversation between Algren and Taka's oldest son, where they both admit being scared, ending with the boy begging him to just go already as they both try not to cry. The hug makes it even worse.
Values Dissonance: The audience is supposed to sympathize with the rebellious remnant of what, art and culture aside, amounts to a hereditary caste of armed thugs who retained carte blanche to abuse and kill commoners for offenses that we would in modern terms find ridiculous and petty. Rendered mostly superfluous during the relative peace of the Tokugawa shogunate, samurai either spent their time absorbing resources produced by the peasants and prosecuting internecine conflict or were pressed into the role of bureaucrats- the forerunners of the modern Salaryman.
Also in universe, as much of the Character Development and plot advancement come from comparisons between Japanese and Western approaches to honor in combat, and in general.