Here is why I think Katniss is a Mary Sue
1. Girls raised on near-starvation diets end up with bone deformations, bad teeth, and thin hair. Yet somehow Katniss is starving, but only just enough so that if you slap some makeup on her, she will turn heads.
2. She's the best archer in the whole world. I understand that the author does at least bother to explain why this is the case, but the notion of anyone, even a girl who has spent many years hunting moving creatures with bow and arrow, can pick up a bow, use it for a few hours, and be confident enough to shoot an apple out of a pig's mouth without injuring the people eating behind the pig is kind of ludicrous. All bows take time and practice to get right, sort of like how boots don't feel right until you walk a few miles in them.
3. Katniss is given a range of implausible social skills for a girl with her lifestyle to have. First she is shown to be a kind of loner who doesn't really have any social skills and has major trust issues (to the point that she even doesn't understand something as simple as "this boy has a crush on me, which is why he is nice to me"), then latter she somehow has the natural charisma to lead armies, despite never having an opportunity to learn such skills. Alexander the Great wasn't able to conquer the world because he was born that awesome, he trained under the likes of Aristotle for that role. So who trained Karniss Everdeen to be the spiritual leader of a country the size of North America?
4. All the boys love Katniss. Sure, she only ever thinks of herself and is seemingly ignorant of the notion of affection for others, but that doesn't matter, does it?
5. Whenever something comes up that could and should be a major hindrance to Katniss, she whips out some hidden talent we didn't know about until that very moment. An arena where she has to swim? Oh, despite the fact that basically no one from her hometown knows how to swim, Katniss learned because her special daddy would sneak her out to the special lake that nobody else knew about and teach her to swim (even though the odds of her father knowing how to swim are low to zero).
6. The President of Panem takes far too much of an interest in Katniss, especially in the second book where she poses almost no threat to the government beyond a single small act of rebellion she managed at the end of the first book. So either the guy is just that paranoid about everything or he becomes a Super-Persistent Predator
to Katniss because Katniss is the focus of the book so even world leaders should pay attention to her.
7. The same thing goes for District 13's leader. Why does she make Katniss her enemy? Did she really
think Katniss was planning on taking away her throne? Good lord its like paranoia is confused with leadership skills in this setting. Either that, or Katniss Everdeen is the hero, so let's all worry and fret about what Katniss is doing.
8. The mockingjay pin. The story never adequately explains how, exactly, Katniss is so beloved by the mayor's daughter that she is given what is probably an ancient family treasure as a gift. Is it mentioned in passing that the two spent some time together once? Sure. Do we actually see the two acting as best friends should? I don't recall that, no. So Katniss is so special that priceless treasures are given to her, even by characters that she seemingly ignores.
9. Even the damn cat treats Katniss as a special thing. While the cat is seemingly a nice, gentle creature around everybody else, it spits at Katniss. Why? Because Katniss is just that speshul.