Arc Fatigue: The Death Zero arc. The arc is a huge Secret Test of Character from Hao to Hana, in order to teach him that being strong is more than reckless strength, fighting must be done with a purpose and to get him a brand new spirit partner. The whole arc happens inside the Great Spirits, most precisely, Hell; but people are getting tired of the slow progress and really want to know what are doing the living members of Team Hao right now.
Author's Saving Throw: Hao being a massive Karma Houdini in the original series is addressed with the revelation that he's not Easily Forgiven and many of the previous Shaman Kings are understandably not pleased with a mass murderer like him in that position. On the other hand, the current protagonists are being forced to help him keep the job.
Hana. He is liked because he is a mesh of all the traits of Yoh and Anna and a more assertive protagonist, but there's also the portion of the fanbase who dislike his bratty attitude and short temper.
Allumi. While she acts as a foil for Hana and keeps him grounded like Anna had Yoh from not doing anything, many vocal fans dislike her for many reasons. The ones who disliked Anna in the original series see her as her clone (not helped that she was initially called "Anna The III"). The others feel like she is a tacked on Mary Sue — she's the daughter of Silva, who was never established to have a family or a significant other, and for some reason decided to raise his daughter to be an Anna clone, and that she always seems to be ahead of everything and knows what to do at every time. And there's also her lack of chemistry with Hana or a justification for their engagement, as she is as abusive as Anna, but without her backstory with Yoh, which was properly developed in the original series.
Designated Hero: Hao. While he's criticized by previous Shaman Kings for his actions, he's still meant to come off as the Big Good of the series and the protagonists are fighting to let him keep his position as Shaman King despite him being completely unrepentant for his actions in the original series.
Tamao became this when Funbari no Uta was released, as she stopped being a Shrinking Violet and turned into a certified badass — She had to be Surrogate Parent for Hanna at age 14, became a school delinquent and at age 17 she and Ryuu whipped out all the gangs of the region. Many fans wanted to see her progression instead of Hana's.
Fridge Brilliance: Hana has more power than his father Yoh had at his age. Considering that Hana died as a baby, dying is the best way to increase furyoku (spiritual power) and we don't know how much time passed before Hao revived him, is understandable.
They Wasted a Perfectly Good Character: Many fans of the original series wanted to see how the lives of the original cast (except for Tamao and Ryuu, who are supporting characters) went, like Yoh and Anna's mission around the world, how did Ren and Jeanne got together and had Men, or Lyserg's life at Scotland Yard, or Chocolove atoning in prison, or Horo Horo doing more things outside of having a brief cameo.
They Wasted a Perfectly Good Plot: Rather than having any kind of sympathetic Freudian Excuse, Yosuke Kamogawa and YVS are pretty much just assholes. In fact, the former not being a "real" shaman is often seen as a lazy cheat to make him flatly evil, since the original manga frequently stressed that all shamans are good people deep down; some have just lost their way.
Unintentionally Unsympathetic: Hao is more-or-less the same genocidal jerk he was last time, just more patient about waiting for humanity to destroy themselves. And while the various previous Shaman Kings have put forth a voice of no confidence in his leadership and started a new tournament to pick a different Shaman King, the audience is still, unfortunately, supposed to find Hao the most sympathetic option, and the author has turned the previous Shaman King into an amoral monster to both make Hao look better by comparison and extend the work's long-time anti-capitalist Green Aesop.