This began as a reply to a Facebook post, then became it's own Facebook post. The problem is that both of them are in a secret group so people can't link to it unless they're part of the group. This flaw has now been rectified by my re-re-posting it here.
By the way, there are massive spoilers left completely unprotected in this post. If you haven't seen Star Wars: The Force Awakens yet and care at all about being spoiled? Go back. This is not the place for you. This post is also in response to an article that was linked to in the secret Star Wars group, which I have reproduced below. You can read it yourself, of course, but the short form is that the author criticizes Rey for being a "Mary Sue".
I disagree.
So here's the thing. The term "Mary Sue" has a fairly specific origin and original meaning. Back in the day, Mary Sue was a reference to a specific Star Trek fan fiction where an author made a self-insert character modeled after herself, or perhaps more accurately, an idealized version of herself, into a Star Trek story of her creation. In the story, Mary Sue was a better leader than Kirk, smarter than Spock, a better fencer than Sulu, and prettier than Uhura. Everyone adored her on meeting her, and both Kirk and Spock fell in love with her. She solved all the crew's problems with a deft insight and she made everything great.
She was a character without flaws and as such, was boring as all hell.
Having a perfect protagonist is an easy mistake to make for a new writer. Doubling down on a character's perfection by having them solve all the problems kills the drama of your work. It's something you have to work through as you develop as a writer. Mary Sue's original creator wasn't a professional writer. She was just writing some fan fiction to be published in a fanzine. She can be forgiven for making a new writer's mistake because she was a new writer. It happens.
(Less forgivable is having a Mary Sue appear in professional work. Track down a copy of the 1985 Star Trek novel "Uhura's Song" by Janet Kagen to see a Mary Sue in action.)
What then defines a Mary Sue? Really, two components.
One is that the character is essentially perfect. Either they have no flaws at all, or they've got a tacked on flaw that in no way impairs the character's function. Examples of the later often include things like artificial self-doubt ("Yes, I am the greatest star admiral in human history, but I made one mistake, and how can I trust myself EVER AGAIN?" *cough, cough* Honor Harrington *cough*) or even more galling, the fear of one's own abilities. ("I've saved the Alliance so many times that the corrupt government has tried to murder me and all my friends, but I dare not overstep my bounds lest I become the mythical hero "Black Jack" that everyone accuses me of being!" *cough* fuckin' Black Jack Geary *sputter*) The problem with those "flaws" is that they never actually impact the story in any significant way. Sure, Honor may have moments of self doubt that she talks over with her (sigh) telepathic tree cat companion. Yeah, Black Jack Geary is terrified that he'll lose control and will conquer the universe. But in both cases as soon as the action starts, both "flaws" are immediately ignored and the character's perfection shines through to lead his or her forces to victory.
Which leads to the second part of being a Mary Sue. A true Mary Sue distorts the story with their perfection. You see, it wasn't just that Mary Sue was so beautiful and wonderful that everyone loved her, it was that she killed the drama of the story by having the perfect solution at hand all the time. She existed so the Enterprise could be in danger, then she'd tap a few buttons, then Spock would say "Astonishing. I would never have thought to <insert technobabble here>. Truly you have an astounding intellect."
Right. A Mary Sue (and her gender flipped counterpart, sometimes called a "Marty Stu") isn't just a perfect wish-fulfillment character, but is one who breaks the story with that perfection.
With that in mind, is Rey a true Mary Sue?
Let's start with her being "perfect". Well, she's a skilled mechanic. But she's spent most of her life disassembling a Star Destroyer to buy food with the parts, so she should be pretty good at it by now. And it's heavily implied that she poked around in the Falcon a lot over the years, so her familiarity with it makes sense. She's a good pilot, but that probably comes from her Force powers. After all, both Anakin and Luke used the Force to make themselves better pilots. She's a lightsaber master? Well, no, she really isn't. For most of the fight with Kylo Ren, she's on the defensive, running for her life or barely blocking Ren's attacks. Further, we should recall that Ren had just been shot by Chewie and was pretty much getting by entirely on adrenaline and rage. And while Rey seemed to have the upper hand right before the earthquake brought the fight to a close, there's no guarantee that she'd have won in the end, or further, that a healthy Ren wouldn't have cut her to pieces as quickly as he had beaten Finn.
How about emotionally? Well, her sudden terror at the Force vision that she's over by the time she mind tricks James Bond does have the feel of a tacked on "flaw". While Finn being attracted to the first pretty girl he's met who wasn't also a Stormtrooper makes sense, Han seems awfully quick to try and hire her. And it did seem odd that Leia hugged Rey, a girl she'd never met before, instead of Chewie, the friend who'd she'd known for decades and the one being in the galaxy who probably was hurt more than Leia herself was by Han's death. So that could be something...unless, as I suspect, Rey is Luke's daughter and neither Leia nor Han was willing to admit it publicly yet. In which case Han wanting to look after his niece, and Leia comforting her niece makes perfect sense. Also, I'd argue that she's impulsive, quick to anger, and doesn't really plan ahead the way she ought to.
So it's kind of iffy if Rey is perfect enough to be a classic Mary Sue. How about her distorting the story with her perfection?
That's an even more dubious case, really. Rey doesn't actually do all that much. Finn's the one who forced Phazma to lower the shield. Poe Damaron's attack and the bombs placed by Han and Chewie are what blew up the Star Killer. All Rey managed to do was get captured, escape, and keep Kylo Ren from killing her and Finn. And yeah, that was important, particularly for the future films, but it's not like Rey had an easy time of it, wasn't challenged, or made everything better by being perfect. Hell, the end of the movie doesn't actually have the good guys in great shape. The Republic's gotten its head blown off, most of the Resistance fighters got shot down over the Star Killer, Han's dead, Finn's in the hospital, and about the only positive is that Rey found Luke at the Irish Jedi Temple.
Therefore, I have to conclude that by the original meaning of the term Mary Sue, Rey really isn't one.
tl;dr - No, Rey really isn't a Mary Sue.