There's more to it even than that. One-dimensional perfection (within the context of the story; "flawed" characters whose flaws are treated as meaningless still

There's more to it even than that. One-dimensional perfection (within the context of the story; "flawed" characters whose flaws are treated as meaningless still quality) is an important aspect of Mary Sues, but it takes more than that to be a Sue. Perfection is, in fact, one of three critical aspects. The second critical aspect of a Mary Sue is being unnaturally placed at the center of the plot. The "unnatural" part is important: a character who makes sense as the focal point of his or her own plotlines is not a Sue. This is what makes Sues in fanfiction easier to spot than Sues in original works: you can compare a fanfiction to the original story, and see if it flows the same way. When the work itself is original, you have no basis for comparison: you have to look at more subtle (but, in some ways, more egregious) flaws in the writing. It happens, but it's easier to mask. All Sues are wish-fulfillment characters, but not all wish-fulfillment characters are Sues. The difference between them brings us to the third critical aspect. Most wish-fulfillment characters represent the reader, but a Sue, by contrast, represents the author in particular. Authors and readers can of course have the same fantasies -indeed, some would say the entire point of fiction is to make this happen- but a Sue gets too intensely personal, to the point where it becomes harder for anyone but the author to relate to the Sue: it breaks the rapport between the character and the reader.