Where I find Mary Sue's the most evident is when there's a huge discrepancy between the what the character does and how they act and how the rest of the world treats them. Something like everyone loving them for no good reason. A big example is Ana Steele from 50 Shades of Grey. There is such a big difference in way she acts, and how everyone treats her. She is such a massive dick to her best friend, but the book expects you to think she's great and her friend's just annoying, she isn't funny at all, but Christian considers her very witty for inexplicable reasons (note that I haven't read the book, just read this [http://jenniferarmintrout.blogspot.com.au/p/jen-reads-50-shades-of-grey.html?zx=67317b32c1f8ef73] review, which happens to be full of excerpts, more than enough examples to judge this on).
Another one that you mentioned that does this is Katniss, at the very least in the second movie (read the first book, but that was a while ago). Everyone makes her out to be incredibly important, and such a badass, but...the second the action starts she's just so useless. She takes care of mooks, but any time they're in real danger she's either being saved, or sitting by and watching someone else save them. There's one moment that she does something to resolve a problem, the rest of the movie she's pretty useless, and constantly in need of saving.
It's discrepancies like that where it really bugs me. And it really feels like an author insert. The author's trying to make the character act like them, but is having the entire world make a really big deal about that.
Male Mary Stues tend to act a little different, they will still have the world make a massive deal about them, but it's less common for other characters to praise them for doing nothing. More often you'll see their actions painting them as absolutely infallible.
At the very least this is what I've noticed in my experience. There's always a group that tends likes these characters though, and the fact that male directed media stretches across genders more than female directed media means that fewer people are going to be part of the group that loves the Mary Sues. Being on the outside of a fandom makes it a lot easier to criticize it. So, maybe part of it comes from that?
I'd also bet on a suggestion I saw someone make earlier in this thread, that most fanfiction writers are female. Considering that that's where the trope started, and I can't think of many Mary Sue characters in actual professionally made stories, I wouldn't be surprised if there just existed more female Mary Sues in the plethora of poorly made fan fictions