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.
The director specifically states it's a commentary about East African child armies, so probably the Southern Peoples' Liberation Army (currently ruling South Sudan) and the Lord's Resistance Army (the infamous Ugandan rebels). What happens to Sara is a particularly strong parallel with the LRA's treatment of girls as non-combatant sex slaves.
Complete Monster - King Hamdo is a raging and unpredictable tyrant who uses child soldiers as cannon fodder. Hamdo evokes the smallest drop of sympathy because he is obviously insane and in great pain - and then he kills his cat in a temper tantrum and sexually assaults a little girl. His second-in-command warns him that one of his tactical moves will directly result in the bloody deaths of thousands of children, and his response is, more or less, "So?"
Crowning Music Of Heartbreaking - As he proved on the Rurouni Kenshin OAV soundtracks, Taku Iwasaki's music WILL make you want to sob in the corner just by listening to it.
Ensemble Darkhorse - Some fans actually complain that the story follows Shu instead of Nabuca.
The dark-skinned, blond-haired boy in Nabuca and Tabool's corps has a surprising amount of Japanese fanart, as does that corps' drill sergeant.
Foe Yay: Tabool's unhealthy obsession with Nabuca and subsequent rage whenever Nabuca rejects his attention are typically interpreted as an example of this.
There is definitely some tension between Shu and Nabuca.
Fridge Horror - The director specifically says he was inspired to write this anime by the Rwandan genocide and by extension, Africa and the Third World's particularly brutal dictators and civil wars. Of course, in real life, there weren't just the infamous Idi Amin or Ferdinand Marcos making hell for their people; there were plenty other brutal strongmen who didn't stand out quite as much in Western media. In other words, especially considering the environmental hardships Earth is facing in NTHT, Hamdo probably isn't the only brutal, power-hungry strongman out there.
Fridge Logic - How are Sara and Shu able to talk to each other? It's highly doubtful that Sara's fluent in Japanese and Shu in English, and for that matter what language does everyone in Hellywood speak? How are Sara and Shu able to speak to them?
Another question is why they don't use the time machine to get water.
I thought it was assumed that the time machine requires a lot of energy to use, and the limited amount of matter it can retrieve at a time wouldn't be enough to break even.
While the story only involves the conflict between Hellywood and Zari Bars, it seems logical that there are countless other settlements all over the world, located at many different altitudes, depending on where the water is. One might wonder what happens at the end of the show to all of the settlements that were located below what would become sea level. Oh those poor Ewoks.
The abortion for Sara may actually have been a non option seeing as the doctor who recommended it, and the only doctor we've seen in the series, was shot dead, and no other was mentioned.
Moral Event Horizon: King Hamdo has a few, before the series started, he had abducted numerous children, put them into combat and destroyed their villages so they can't go home. Other examples could be Ordering Shu tortured.
Tabool shoots Nabuca and kills him without showing any remorse, showing that the years under Hamdo has broken him and turned him to Hamdo's ideals.
Elamba shooting Sis and the Doctor, leading to both their deaths shows just how far into He Who Fights Monsters he has descended after all the fighting.
Tear Jerker - Most of the series, but especially the last two episodes.
The Woobie: All of the main cast have their moments of this with the exception of King Hamdo, but Sara especially stands out in this category.