The Anatomy of a Mary Sue

I failed another Mary Sue test. Apparently, I 'should probably think of ways to tone down this character a little to make him or her more realistic'.

Now, since I have yet to actually vanish in a puff of logic, I'd hazard to say that Sue-ness is more complex than a checklist of character traits. Blogger Jennifer Koch (aka novadestin) has written one critique of Mary Sue litmus tests, and I'm inclined to agree with many of her points.
First of all, a lot of 'Sue' traits can be completely justified within the setting or within a particular story. This is particularly true of sci-fi and fantasy, where characters' unique status is often a major plot point, and of escapist genres where we want everyone to be above average. In these cases, a character can be a bit over the top--or even a lot over the top-- and fit right in with world of the story.

Second, a heap of stereotypical Mary Sue traits do not preclude character development. For example, a number of characters in Neal Stephenson's Baroque Cycle have all kinds of 'Sue' traits, but still manage to be likeable. Part of this is that their human sides are developed, and part of this is that they don't cruise through the plot unimpeded-- their extraordinary abilities are matched by extraordinary challenges.
Finally, I firmly believe that what makes a character a Mary Sue is not their specific traits, but their effect on the story around them.

Fundamentally, Mary Sue tests fall short because they focus disproportionately on superficial character traits (unusual names, etc) and authorial identification with the character rather than how the character interacts with the plot and setting. A story can be derailed just as thoroughly by a character with no extraordinary features who breaks the rules of the setting with impunity and is the moral centre of the fictional universe as it can by an escapee from House Sparklypoo. It's up to you to evaluate whether or not any one character is being treated as awesome by the narrative in the absence of any evidence, or if a character is getting away with undue rule-bending.