Things like Eirin getting sick (An immortal's body is immune to all disease, by Mokou)
This is inaccurate. We don't even know if Eirin is immortal or not. There is no canon proof on this part.
Toyohime wanting to take a rabbit to the moon (which would "taint" their precious, pure moon)
Does not contradict with canon. They do have a ritual cleaning in which you can clean impurities. Lunarians used to be humans from earth. They would have "tainted" the moon ages ago if there was not a way to cleanse themselves and others.
Kaguya getting stuck on bamboo, and being physically unfit (she's supposed to be physically strong, according to Marisa), getting "fat" ("Souls don't have a particular size, so they can freely create another body wherever they like", by Alice), the weaponry in Kourindou.
Kaguya does not care enough to destroy the bamboo. It isn't like being stuck hurts her.
That said, let's not forget that it isn't that she isn't physically fit, it is that she is psychologically lazy. She can easily do a stretch that is impossible for even fit people, but can barely touch her knees with her hands.
Everyone has a soul, souls don't have a particular size, but the body has a particular size. If souls can freely create a size, then anyone, not just Kaguya can be of any size they want. What the Hourai Elixir does is causes the soul to become invincible. It doesn't actually change a soul's state.
What about the weaponry in Kourindou? Guns is not something that is out of place. Those are probably weapons that imaginative designers tried to do, but failed, because of impraticality and thus it fell into fantasy lands.
On Reisen: she's not equal to the rabbits.
"Tewi Inaba acts as leader of the rabbits, but she gives orders to Tewi
This makes her the de facto leader of the rabbits."
This is false. Reisen cannot give orders to Tewi. Eirin never gave Reisen the authority to do this. However, Reisen takes it upon herself to order Tewi, even though she isn't supposed to. Her thinking is probably on the lines of since she is Eirin apprentice and she believes Eirin is the boss, then she would have authority over the rabbits. This is untrue and we know this from canon, not just from Inaba of Earth/Moon.
If you check other canon sources, like Cage in Lunatic Runagate, Eirin does not order Tewi around. When Eirin first met Tewi, they made an agreement, not that Eirin was Tewi's boss. The relationship between Eirin and Tewi are of equals, not of a superior and a subject. Eirin does not actually have authority to order the rabbits around, only Tewi can do that.
Here is the link:
http://en.touhouwiki.net/wiki/Cage_in_Lunatic_Runagate/First_ChapterOn Eirin: threatening or killing someone (even worse if they're just "tools", like the rabbits) is not being sadistic. Bdsming Reisen to the point where she can't get up in days, is.
As I have already mentioned, Reisen deserves a lot of this. Refer to that link to see why.
All of her background, like living for over a millenia, being a good talker with an "outdated manner of speech", her feud with Mokou, her supposed "actions" in instants was ignored or altered by the author (which is also true to many other characters... but I don't want to extend this too much).
Mokou may have a fued with her, but for Kaguya, it is just fun and games. This is verified in Cage in Lunatic Runagate.
I don't see anything ignored, you may want to check out Cage in Lunatic Runagate if you are seeing some differences in characterization.
Yes. Complementing what I was saying above, if there's one, may ZUN write the scenario, like he's doing in Ibarakasen.
Just adding this in, I don't hate the Inabas, it was a good read - I just dislike the idea that what's there may be definitive, to be taken into account if there's another work with the Eientei people.
I am saying that there is not much wrong with the accuracy. Yes, some stuff are inaccurate, but most are good. Some get verified in other canon sources.
As I have already mentioned, Cage in Lunatic Runagate talks about Eientei and I believe Zun wrote that.