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.
Angst? What Angst?: Yoh. With a few exceptions, not much seems to bother this guy. Not even being killed (so that he can get some literal Training from Hell, though he wasn't informed of this beforehand).
Well except for that one time when Faust dissected Manta, who at the time was his only friend. That being said, though, he managed to snap out of that funk after a volume or so.
Subverted, Volumes 19-20, show he wants to cure Anna of her Emotion Bomb powers and make Matamune a new Over Soul so he could never see him again, showing how much of a woobie and Stepford Smiler he is.
Anti-Climax Boss: Several. Most notably near the manga's end where the end of the Patch officers' battles are skipped.
Lyserg as well. Some forgive him his trespasses, others do not.
Anna is probably the biggest one, as while some love her, others despise her for her abusive Jerkass tendencies.
Hao gets this too. There are those who like him and those who do not. The ones that don't like him are due to being an overpowered villain (especially in the manga), hypocritical, having a arrogant Social Darwinist type attitude, and a Karma Houdini in the manga. Even with his back story in mind, these fans feel it doesn't excuse Hao's actions. In fact, the list described from before makes some fans see him as a more unsympathetic person.
Ho Yay: To say nothing of Ryu's obvious feelings toward Lyserg, many of the guys fall into this. Notable cases being Ren/Horohoro, Amidamaru/Mosuke, Hao's devoted followers, and some subtext between Manta and Yoh. The omake introduces some with Lyserg and a new character, Hudson. Fridge Brilliance on the creator's part, especially if you've seen the latest Sherlock movies.
Macekre: Actually not too bad, considering 4Kids' track record, but... changing Hao's name to Zeke? Seriously? He's an ancient godlike shaman from medieval Japan, not a trucker! Also, there's the minor fact that Ren, the Chinese shaman, has a British accent while Lyserg, the British shaman, does not...
Also, Horohoro preferring to be called Trey Racer? What?
However, despite a number of name changes (Ryu/Rio, Manta/Mortimer, Over Soul/Spirit Control, etc.), they retained the original name for a shaman's spirit power, "Furyoku", while the VIZ translation of the manga changed it to the more generic "Mana".
Opacho, big time. Also, the X-Laws, particularly Lyserg and Marco.
Too Cool to Live: Most of the human ghosts were this, Mikihisa in the future, and Matamune the split tail cat.
Matamune was one of the few ghosts and characters in general to be genuinely humble, very wise and witty. He displayed amazing powers against the Oni and soon disappeared into the spirit realm this was because his mana for existing on the material world was fading, and seemed to imply that because of his predicament, his powers were much lesser than 500 years ago. If Yoh had continued to use Matamune as his ally, it would've been much easier to go through the preliminaries.
Villain Sue: Hao. He still has a decently-sized fanbase though, so mileages vary as to how much this trope affects his character.
Can reincarnate himself if killed, which for most of the series isn't even presented as possibility despite all of his enemies, and by the end, rather than plot device introduced that allows him to be killed for good, he instead makes Heel-Face Turn, effectively meaning he gets away with everything he did despite crossing the Moral Event Horizon a dozen times over before the series even began.
This Karma Houdini even becomes a plot point in the sequel, as the previous Shaman Kings are understandably not happy with Hao being the new Shaman King.
This problem is corrected in the anime where he is killed off for real thanks to a plot device.
One of the few good changes: Renaming Chocolove to "Joco". The original name is both unwieldy and potentially offensive, while Joco sounds like an actual name as opposed to a racial slur. (Of course, this was done in the official manga translation as well.)
In the VIZ manga, Chocolove's lips were also edited to match those of the rest of the cast as opposed to the large, thick ones he originally had. It pays to be racially sensitive and it was initially pretty offensive. In the anime, the lips remained (which is weird considering 4Kids' rep...).
Most African-American characters or those with similar heritage received the same treatment throughout the manga.
Averted big time in the Mexican Spanish dub of the anime, and also in the Mexican Spanish manga translation. In fact, the Mexican Spanish dub of the anime makes Chocolove even more offensive (and funnier) by giving him a Southern accent (who is normally reserved in Mexican Spanish for hillbillies or Native Mexicans alike). There are times when Horohoro is racist to Chocolove in the Mexican dub but these lines are really short lived.
They Wasted a Perfectly Good Plot: Yoh is Hao's twin but we never get to see Yoh developing a power similar to Hao. In the manga Hao says that he wants to consume Yoh's soul but we never get what will he win.
This is later rectified in the anime when he does manage to consume Yoh's soul and appears much stronger for it. Until Yoh frees himself and Hao's strength decreases accordingly.
The Woobie: Each of the characters can be seen as this, especially Ren, Anna and Lyserg. Yoh seemed to not be this but Volumes 19 & 20 proved this very wrong, after losing his first spirit ally and friend outside of the household.