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.
YMMV: Fruits Basket
Canon Sue - Tohru, depending on who's watching/reading and his/her source (and sometimes, their pairing preference). More likely in the anime, since it didn't show her manga-mostly dark side composed of serious abandonment issues. Then again, at that point, she wasn't the only one...
She goes into Stepford Smiler territory pretty damn fast once the manga gets past the point where the anime stopped (or diverted from the manga). After that she pretty much becomes a deconstruction of a Canon Sue, and all her painful backstory and insecurities come into light, and the horribly self-destructive psychological scars get dug up and shoved down her throat. Break the Cutie oh so much. The anime on the other hand... well see below in the Fixer Sue entry.
Complete Monster: Ren Sohma, natch. See her entry in the anime/manga page of the tropes page for more.
Kyo's father to a lesser extent if you think about it. After Kyo's mom committed suicide, it was believed that it was Kyo's fault. However, it is later implied that she loved him and that Kyo's father may have been the cause. He took no responsibility and blamed Kyo for it.
Fandumb: There's a good chunk of the fanbase who use to be Akito fangirls, but who now despise Akito after her actual gender is revealed. Rin also gets this from Hatsu fangirls.
Fixer Sue — By and large, Tohru plays super-psychiatrist through The Power of Love, making her perhaps this more than a Purity Sue... but since the audience generally really, really wants these things fixed, most are charitable enough to give her a pass on it. After all, for all the tragic past in the story, it really does land far on the idealistic side of the Sliding Scale of Idealism Versus Cynicism.
Subverted ironically by the fact that Tohru's Fixer Sue nature is actually one of her major character flaws, stemming from her personality as an Extreme Doormat, which itself is probably derived by the utter disdain with which she is treated by the rest of her family (except her slightly senile grandfather) after her mother's death. As a result, Tohru's desperate need to make other people happy reaches almost pathological levels to the point that she will neglect her own health and well being for the happiness of others; a fact that becomes more poignant with her revelation as a Stepford Smiler later on in the manga.
Fridge Logic: Wait, a minute, Hatori is completely blind in one eye. Why is he the most competent driver?
Well clearly, Shigure is so horrible a driver that a man blind in one eye is better behind the wheel than he is.
And the other people old enough to drive would be Ayame (Hatori at one point refuses to let him drive), Ritsu (ha!), Rin (probably hasn't had time to learn), Kagura (possibly) and Akito (who gets Hatori to drive)
Magnificent Bastard: Shigure. He spent a very very long time manipulating and screwing people around trying to ensure that at the end of it all, he ended up with Akito. And he reallywasn't nice about it.At ALL.
For the first quarter of the manga and anime certainly, but after Cerebus Syndrome kicks in and she goes through the Trauma Conga Line, you'd be really hard pressed to argue for anything other than Woobiedom.