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.
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.
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.