The third Saint Beast has almost no presence in the plot; in fact, he could easily have been removed from the story arc with little effect. His only role is to kill the second Saint Beast (Who had apparently been killed by Kuwabara moments before; had he been actually dead, no one would have complained), and then be killed by Hiei in one of the shortest fights in the series. However, it all makes sense once you realize that Hiei was originally supposed to be a one-shot villain, but became so popular that the author wrote him back into the story. In order to do so, the author had to make last-minute changes to the plot so that Hiei would have something to do — and since all of this was added in at the last minute, neither Hiei nor the Saint Beast he fights have much effect on the plot of that story arc. Although Seiryu would still need to appear if Hiei hadn't been brought back as he and his fellows were based on these constellations.
In the anime, Seiryu did serve the purpose of showing that while he has been a cold blooded killer, Hiei still has honor, and doesn't take kindly to killing a comrade. If anything, Hiei is loyal.
Hiei could also be angry against an ice-user since he was abandoned by a tribe of ice apparitions.
Kido was able to capture Yusuke, but only because Yusuke didn't know what he was up against and Kido simply outwitted him - he didn't have that advantage every other time.
On paper, Kaito's powers are absolutely broken. But he never really uses them against their opponents because they have a glaring weakness: Everyone within his territory is affected. Which includes not only him, but also his allies. This makes weaponising his powers incredibly risky. So by simply offering his booksmarts and not his powers, he's actually doing the team a favour.
Apparently, spiritual awareness (being able to perceive ghosts and demons, and possibly the broad definition of psychic powers) is uncommon/rare in modern times, perhaps passed through family bloodlines (as implied by Kuwabara's sister). Yusuke's ancestor may have had some powers, judging by all the poisons in her bodies. So were the more common in the past? Perhaps so - because the Kekkai barrier either hadn't been erected yet, or it wasn't as strong. The reason people in Mushyori city develop powers is because of the energy radiating from the demon world - in the weakness in the Kekkai barrier.
During Raizen's flashback showcasing how he met the Lady Doctor (Yusuke's human ancestor and how the two of them are connected biologically) he's clearly on the run from a group of humans and is wounded. At first this may seem like Fridge Horror since you're wondering what sort of enemies was Raizen fighting in order to render him weak enough that he'd be on the run from a bunch of humans? But remember that Hokushin informed Yusuke that demon law (at least in Raizen's country) states that high level demons must wear an organic device that suppresses their power to minimum levels so they can get past the Kekkai Barrier. There are other methods but they aren't heavily elaborated on. Point being: Raizen may not have been at his best when he was wounded on Earth due to this method.
According to the wiki, the Kekkai barrier hadn't been erected yet. So maybe it was a little bit of both - he might have been less powerful due to having been wounded by the humans (on the run from him) but he also may have simply not been powerful enough.
During Genkai's succession tournament, she states that she cares not whether the champion will use her powers for good or evil, only that they win and her techniques can be passed on. At first, this makes Genkai come off as a cold sociopath. However, in retrospect, Genkai says this because it literally doesn't matter; nobody evil could receive Genkai's power. Genkai's final test before passing on her power is to determine both her student's morality and determination by proposing that they must kill her. If her student immediately refuses, they do not possess the determination to get stronger. If her student immediately complies, then they do not possess the responsibility to handle such power. Prior to her power transfer to Yusuke, Genkai was the third strongest being on Earth, behind only Sensui and Younger Toguro. Even in the highly unlikely event that the student would be able to kill Genkai, her secrets would die with her. Rando would have never succeeded Genkai in the first place.
So where does Kurama get all these fancy outfits that he wears over the course of the series? They can't be his mother's right? Forgetting how opulent they are, there's no way his mother wouldn't take note of the various gashes and blood marks on the clothing. Well that's obviously ruled out. It's far more likely that it's a combination of factors. As a thief Kurama has stolen many things over the course of his long life, so they might be left over clothing that he stored away somewhere and just has a lot of surplus. He's no doubt very rich from all his thieving, and likewise probably has a lot of treasure stashed away, so it wouldn't be surprising if Kurama actually purchased the clothing. Or since Kurama materializes a white shirt and pants, and shoes when he goes into his fox demon form then he might have the limited ability to materialize or "poof" the clothing into existence. Whatever the case, Kurama certainly likes to dress in style.
It seems like Kiyoshi Mitarai (the Sea Man) loses about a hundred IQ points when he becomes a "good guy." Apart from playing some tennis, he mainly just stands around and looks pretty for the entire rest of his appearances in the series, despite the fact that he's the only one who could have easily defeated Sensui in combat. His power is to use his blood to summon water-monsters from any existing water, which are invulnerable to normal attacks, and which can envelope you. When they do this, you're trapped in a separate dimension, made entirely of water, and can only get out if you have an attack that can break through dimensional barriers. We know that Sensui doesn't have such an attack, because if he did, he would have broken through the Kekkai barrier by himself, instead of needing to lure Kuwabara into doing it. So, why didn't Sea Man just create a large water monster with his blood, use it to envelope Sensui, and drown him within ten minutes? Seems that would have solved their Sensui problem pretty neatly, to the point where he couldn't have escaped like he did, especially since the first thing that Sea Man does after escaping from the Uraotoko is to land in a huge pool of water.
Fridge Brilliance: His powers aren't instantaneous - and presumably? No Ontological Inertia is in effect so maybe the water monster(s) would vanish without anyone giving them orders. If he attempted this, Sensui would know to go straight for him.
Sensui's parting words to Yusuke "I needed to collapse those boundaries between us and them, thus the tunnel, but then I saw you Urameshi. First demonized in a human's body, and then humanized in a demon's. You dissolved the barriers between us in ways I never imagined." equally apply to Kurama's life. He possesses a human's body in order to survive, and then slowly demonizes the human's body altering it into a demonic form that looks human but isn't. Then through interacting with humans he learns about love, honor, and compassion and the demonic mindset he lived by for untold centuries is eroded away at — making the ruthless bandit a loving, hardworking, and passionate young man to an equally kind mother. The humanized demon is then given a chance to return to his demon form and resume what he once was (demonized as a human) but then struggles with the idea that he can continue to remain as the good person he's become if he maintains that form, thus choosing to be human (humanized as a demon).
Consider for a moment that much of the rigid views that led to Sensui's mental collapse may have been trauma in and of themselves. Since demons were attracted to his power from a young age he effective became a Child Soldier fighting a war no one else in his life could help him with or even see. Think about what that must do to a child, was his view of the world dogmatic or was he holding tight to the simplistic justification of a little boy trying to rationalize the fact that he has to kill constantly just to stay alive. Could he not take that the world was "gray" or was it that the way he'd been reassuring himself that he wasn't an evil person for all of his life was shattered in the most brutal way imaginable. Given the jaded man we meet when we see the real Sensui this was as much about his own self-image as any big picture morality.
The naming conventions used among the main cast is interesting when viewed through the lens of Western and Japanese naming conventions. In the West, you normally only call someone by their last name if you're very dismissive of them as an individual, and you're saying they're so low class that only their family name has any value. In Japan, by contrast, referring to someone by their last name is seen as a sign of respect since you're acknowledging that their family name brings them a sense of honor and worth. Kuwabara constantly referring to Yusuke as Urameshi and Yusuke constantly referring to Kazuma as Kuwabara is amusingly fitting in the lens of both concepts. Kuwabara and Yusuke both respect each other as rivals, hence the last name usage, but neither of them are ever openly affectionate enough around one another — even after becoming friends — that they feel comfortable referring to one another by their first names. In the case of Hiei, his clan abandoned him when he was born so he has no clan name to be addressed by. And in the case of Kurama, even though he has a human name, everyone respects Kurama enough that they can refer to him with such a familiar term.
In the last volume of the manga, we find out about Enma brainwashing low-class demons so that they would attack humans and he could justify his power over the human world as protecting it. In retrospect, Hiei stealing the Shadow Sword and kidnapping Keiko seems extremely out of character for him; his goal has always been to find his sister and his tear gem. And this is to say nothing of the cackling supervillain act he puts on. Flashbacks show him always being the same somewhat lowkey guy we've always seen. Is it possible that he was a victim of Enma? If so, kick in the fridge horror: Hiei might only be alive because Koenma thought Yusuke needed backup against the four beasts and paroled him. And Koenma also immediately followed that mission up by sending Yusuke to rescue Yukina, because Yusuke owed Hiei. Hiei and Yukina both might only be alive and free because Koenma is so reasonable.
We're told that in the past Sakyo and the Black Book Club had opened a portal to Makai to kidnap and sell as slaves minor yokais, and this portal was closed by Sensui ten years before the series. We're also told that Hiei started looking for Yukina at around the same time, but couldn't find her. It's very likely she's one of the yokai kidnapped by Sakyo... And Tarukane grabbed her during the chaos of Sensui's assault.