One of the problems with Mary Sues is that we're mainly told about them, rather than see them do something. We're told they're smart, witty, good in strategy, perfect, beautiful, strong, independent, social, friendly, etc.
Yet with exception of beauty (a lot of Sue-writers do tend to describe their pet Sue's appearance with huge amount of detail), we never see that proved. Okay, maybe the Sue wins a game of chess in the story's background somewhere (not that that immediately makes someone a strategy wiz), and maybe some people laugh at a witty remark of them (though often, the remark itself isn't shown and if it is, it's usually not all that witty), but that's it.
Sometimes, we hear about them doing things that prove those points, but even then, the actual action is rarely shown. "Mary Antoinette Raven Tara Susan "Sue" Blackwood smiled as the strategy she had convinced the others of proved to be working." vs. "I think," Mary said, "that we should reinforce the troops here, because the intelligence we have suggests the enemy will likely come ashore nearby. Perhaps we could set up a trap there for them."
The first only tells us she's good in strategy, the second shows it (or disproves it, depending on the result later in the story).
Of course, it's not a problem if some things are told rather than shown; however, the problem with many Sues is that we almost completely have to rely on things the author tells us, rather than shows us, which makes Sues boring - perhaps even moreso than their supposed lack of flaws, or the sheer predictability of the character and events it stars in. (It also basically makes most Sues a form of unreliable narrating)