[This is specifically referring to the literary area of "fan fiction", but as usual I never quite stay within the lines...]
Physically and undeniably hurts to read it, and all the more so when you know it's being unfaithful to character/time/place/etc. as well. That's why I very rarely hang around any fanfiction that isn't very overtly erotic/intimate, and most-preferably slash at that....because anything that has a hint of authorial wistfulness, mental prudishness or conventional idealism in it tends to overturn the balance of aesthetics in really insidious if not blatant ways. And at least if it's just the 'original characters' developing relationships and making out, that means there's some halfway serious thought that had to go into planning and orchestrating the whole thing--not just plunking in someone new and shoehorning in a romance that has no firm basis in the rigours of actual character psychology.
I hate Mary Sues--I can smell 'em, I can hear their awkwardly eager manner of speech and self-description (oh, damn well do I know their scent after all this time with Ancient Pine Resin...or Pine-Sol, as represents both her Circean-solar nature and the natural desire to wash out all one's direct memory of her after parting ways. Fire may have purified 'salem's Lot, but I'm still working on the appropriate exorcisms for this one...)--and even when there's no one technically there in the verbal flesh, I can tell where her spirit lingers near, meddling and manipulating and making characters do what they never would in any saner state.
That is, the Mary Sue is the manifest Avatar of an immature ego trying to justify itself in words. I will give her that--after all, I was once in that stage myself, trying to make exact mirrors and reinvent the wheel before I started to see the keener and more fragmented reflections of selfhood all around me. Most of all signs in the world of human expression, the blatantly ideal and aggressively omnipresent Mary Sue character is proof that the authors do not yet know themselves as they naturally are, much less well enough to let other people/characters be as they naturally are. Because, of course, the Mary Sue is the center of her own universe as presented to others, and she displaces or warps all existing characters around her to suit her needs, whatever their normal and sane reactions would be to whatever she does--in short, there is never the slightest chance allowed that she will be rejected in the end, that her image will be objectively tarnished, that her dreams will fail, because she's not a real character in the first place--just an intrusion of the power/s-that-be into this appropriated world. Nothing can stand against her, not tradition nor fact nor logic. She is the incarnation of a determined Demiurge, and has all the attendant modesty of Jehovah (no matter what sweet and self-minimizing words may be put in her mouth at any given time--"Why me, out of all the other girls...?"--"I'm just a normal person..."--et cetera, ad infinitum...)
Why her?--because it's likely all the writer has of him/herself so far, and more than anything there's the fear of losing one's nominal "uniqueness"--and therefore every personal detail must be agonised over (insofar as one's capable of agonising), every facet polished exactly in the mind's eye, no matter how little of this preparation will actually cross over into the details of "reality" here. In a more experienced writer or actor this is called building the character--but here, where character itself has not yet been recognised and developed, this building is merely surface presentation, and the object beneath the gilding as insubstantial as a wraith...having as its closest legitimate relative the incorporeal form which tenants and vivifies the blood-soaked vesture and stiffened mask of the Red Death itself.
Edgar Allan Poe knew good writing when he saw it, and knew where to aim the pointer at a story's flaws. And no doubt he would recognise the Masque of the Mary Sue as well, as he had much experience in dealing with the society poetesses and authoresses of his day--I make no judgement as to their literary ability per se--since it has always been a tendency of the feminine awareness, or at least its typical situation, to write forth fantasies where there is no chance to live them out in the physical world. There might not have been the phenomenon of "fan fiction" in his day (unless it started covertly with Werther instead of with Sherlock Holmes), but I'm sure he would recognise the type.
Perhaps he might also--I do need to check my dates to be sure--relate it to a specific character--and one of the most famous in the history of first-person literature, that created by the pseudonymous "Currer Bell", aka Charlotte Bront:e. Is Jane Eyre a Mary Sue?--a governess like the author, poor and persecuted yet virtuous and rewarded in the end with the love of a brooding Byronic hero, her prime flaw being her "passionate nature", and the situations of her life being all-so-closely related to the popular novels and classics of her day?
But the answer there must be a subtle but certain "no"--because Jane Eyre is a real character in her own life, is plain and small and unvarnished and consciously self-doubting as to her own real character, suffers all the mistakes and slips and tarnishments of a real character, does not live in a fairytale world with a fairytale ending but deals with a world of tragedies and unrightable wrongs and disappointments like a real character--no, like a real person, let us say. Her existence is perhaps drawn from that of her creator, but she does not exist merely to live out vicarious pleasures and goals, whether of status or wealth, romance or unbounded popularity. She lives within a fully-delineated/shaded story, and its plot-shapes are not necessarily any kinder to her than to any other character, whatever old-fashioned contrivances within them may catch the eye. Her resemblance to Charlotte Bront:e is one of conscious causality, not of glossing-up and glorification...
And so perhaps Poe would recommend that book, as I do, to anyone looking to get past themselves and learn to write characters with actual skill and nuance and humour and details drawn out of a familiar world. It certainly couldn't hurt...
"Jane, here's your mission...."
("Onegin, Tatiana--you come too...")