There are those who consider it a good addition to the films, those who consider it a good show but prefer to think of it as a separate canon, and those who disown it entirely.
Its place in the Nicktoons canoncity is also debated. Since Nickelodeon co-produced the series in-house with DreamWorks along with The Penguins of Madagascar and later the Monsters Vs. Aliens series, one can consider it to technically be a "Nicktoon," but since DreamWorks owns all of the characters and elements in the series, many seem to disavow it as a Nicktoon due to Nick having no complete control over it.
Hundun crosses this by threatening to kill Po's father just to force him to fight him. This also makes things personal for Po.
Tong Fo counts too, wanting to destroy the Valley of Peace for no apparent reason.
Ke-Pa crosses it when he temporarily killed Po.
Nightmare Fuel: The jumping ghosts of "The Po who Cried Ghost". Those things are hideous and creepy as heck.Their jerky, unnatural movements easily put them into the uncanny valley, and the fact they can raise from their tombs at any time to get you is quite unsettling
Ke-pa. Everything about Ke-pa. There's good reason he's considered The Dreaded in universe.
The Scrappy: Prawn samurai Yijiro has a considerable hatedom for his Ship Tease with Tigress, and it's not surprising at all given the sheer bizarreness of the premise. For many, it ruined an otherwise awesome or/and interesting episode with Japanese elements.
Special Effects Failure: In Royal Pain, there is a scene where an arrow is shot at Meng Tao, who manages to duck and make it hit the rock behind him. When he stands up straight, the arrow clips through his skull.
Squick: Tigress had a crush on Shifu when she was a teenager. He may be her father through adoption, but still...
The Woobie: Po puts up with a lot of crap in this series...
Also Bian Zao qualifies as one.
Holy cow, Peng. His uncle, who he's been seeking for goodness knows how long, was evil, his best friend and idol was thus forced to kill him, and now it turns out the poor boy inherited Tai Lung's dark side. His leaving the Palace and giving up on Kung Fu forever was played completely straight.
Jerkass Woobie: It's not hard to feel bad for Taotie, what with his backstory of being kicked out of the Jade Palace for trying to compensate for his poor kung fu with his passion for mechanisms, having a son who doesn't respect him, being constantly humiliated by the Furious Five, and outright sobbing pathetically at his failures ... however, as seen in is episodes any time he does come out ahead, he immediately becomes a major jerkass, wanting to painfully humiliate Shifu and the Furious Five, up to torturing them to death.