Why does Akira, a normal human being with no samurai blood, have ice powers? He's a shaman, but the Mibu never took him in because 1) Kyo picked him up first, and 2) They would have known he didn't have samurai blood and therefore would have underestimated his potential.
When Nobunaga fights Kyo for the last time, he resurrects the Jyunishinsho to fight for him — but the four strongest (the Berserkers) do not return, and neither does Makora (Sasuke's friend Kotaro). The Berserkers' absences are never explained, but it's theorized that Kotaro refused because he did not want to endanger Sasuke. The true reason becomes clear later, though it's never outright stated: All five of them were Artificial Humans — either experimental creations or Mibu — which cannot be resurrected.
Fubuki never uses the rhythm-matching technique that Shinrei does, not even when he's fighting Kyo, so where did Shinrei pick it up? For a while, it seems that Shinrei simply developed it on his own... and then Hishigi uses it while fighting Yuan. This makes sense for a couple of reasons.
Fubuki is the only one of the current Taishiro who doesn't fall into the Lightning Bruiser category, bordering on Mighty Glacier instead. He doesn't bother moving quickly or dodging — he just blocks and retaliates — so this strategic move doesn't seem to suit him.
Shinrei, on the other hand, is a Glass Cannon. He's strong and agile, but can't take much damage before he goes down. When Fubuki was training him, he must have realized that Shinrei was going to need avoidance tactics.
Cue Hishigi, Fubuki's closest friend. Very fast, very strong, and Awesome by Analysis to the extreme. It's not much of a stretch to imagine Fubuki asking Hishigi to teach Shinrei the basics.
Hishigi ripping out his own heart and then continuing to talk (albeit briefly) seems strange the first time you read it. But then we learn that another Battle Doll (Mibu Kyoichiro, AKA the Sendai Aka no Ou) removed his heart decades ago and has been getting around fine. So it is strange, but at least it's consistent with Mibu biology.
The timeline. Perhaps most blatantly, the ages. It's best to just take the ages of the Mibu as stated in the fanbook as what they look like physically, because it's impossible for most of them to be the chronological ages it says they are. Even the ones who aren't Really 700 Years Old.
For instance, it is not possible for Kyoshiro to be 20 years old if Kyo is 28. Kyo has to be 28 based on the timeline as presented (it's been 22 years since he killed Nobunaga when he was six).
It's also flat out stated that there has not been a single pure Mibu born since Kyo appeared. He showed up when he was six years old, so none of the Mibu who appear in the story can be any younger than 22.
The fanbook lists Yuan's age as 28, but in flashbacks to when he found a 6-year-old Hotaru (who is 22 at the time of the story), Yuan seems to be one of the Taishiro already and sure doesn't look 12. It's never made clear if Yuan is one of the Really 700 Years Old Mibu (like Hishigi and Fubuki, who are listed as 30 and 35, respectively), but regardless, 28 can't be right.
Ruru is revealed in the final chapter to have an "antibody" to the Death Disease. The problem with this is that the illness in question isn't really an infectious disease at all, more of a latent defect in the genetic code of the Mibu Battle Dolls — a defect that is stated to be worse in the "rare breed" experiments like Ruru. You can come up with all sorts of justifications, but as presented in the story (in a single context-free page, no less), it does not make sense.
Sasuke is unable to attack Dr. White, supposedly because he's imprinted and cannot harm his creator. But Dr. White didn't make him, Hishigi did. And Sasuke fights Chinmei later in the series, so he's clearly not incapable of attacking any Mibu.
Hotaru and Shinrei find the bodies of forest-dwellers in the dungeon below Onmyoden, but it's been established that the forest failures don't leave corpses. They disintegrate when they die, like the rare breed children and Mibu. The reason why is a major element of the plot.
The real Kubira says that after his transformation into a Berserker, he had to stay away from his daughter Anju (Antera) because the flesh of young girls is the most tempting to his kind. But the other Berserkers express different preferences (Haira will eat anything, Indara craves the "rare breed", and Mekira wants to eat shamans). The Taishiro intentionally made Kubira want to eat his daughter.
More Fridge Sadness than horror, but thinking too much about that one flashback of Shihodo and Hishigi in volume 28 hurts. They were clearly good friends once, and he actually seems to be making an attempt at a joke at one point. Flash forward a year or two. Muramasa has left the Mibu with Kyo, Hishigi has discovered he's dying, and the King orders him carry out Shihodo's punishment for her "treason" of letting Kyo and Muramasa out of Mibu territory. He can't refuse because he has to protect Fubuki. Yeah. Don't think about it if you care about either character and like your heart intact.
He probably knew Ian well too, and the king forced him to kill her. It's not clear exactly when she joined — probably after the aforementioned expulsion of Shihodo — so they may not have been friends, but chances are he knew she wasn't planning a rebellion.
Try not to think too hard about how bad Hishigi's condition must have gotten before he honestly thought being infested with parasitic eyes was better.
Julian made an immensely powerful weapon (Hakuya) for a swordsman so strong that he broke lesser swords (Hishigi). That sword later killed Julian's wife.