This thread misses a big chunk of the point, I think. The question should never be "Is Rey a Mary Sue?" for some specific definition of the term. It should be "Does the movie do a good job of justifying her abilities?", and the fact is, given that a large percentage of the audience (myself included) walked out of the theatre thinking that she was overpowered, that her abilities did seem to come from nowhere reflects a failure of storytelling on the part of the filmmakers. Not a massive failure - there were other events in the movie that pulled me out more, and other movies that are far, far more flawed. It didn't prevent me enjoying the movie for what it was (a solid, super nostalgic, fun film that I enjoyed), but it is a flaw.
You can make comparisons to other movies, even other Star Wars movies. People have mentioned that Luke seems to be too good of a pilot out of nowhere, but the first SW movie makes the effort to establish that Luke has decent piloting abilities - first he's playing with his model airspeeder, then Obi Wan explicitly says that he's a good pilot, then Luke mentions it to Han, then Luke mentions an example of his skills during the briefing, then immediately before the battle, Biggs confirms it to a Rebel officer, and even during the battle, Luke makes mentions of runs through "Beggars canyon back home". Now, you can argue that Luke's experience shouldn't be enough to qualify him to fly in combat, and maybe that makes sense if you think about it, but that's irrelevant to the experience of the film - it sets up that Luke is a good pilot, then it pays it off. His piliting abilities are effectively a Checkov's gun - it would have been worse to have all those mentions of his piloting ability, and then end the movie with them planting a bomb on the Death Star or something instead of a space battle, because all that setup makes no sense without a payoff.
It's the same with the Force. Luke uses the force successfully twice in the film - once to stop the remote bolts, under Obi-Wan's tutelage, which sets up that Luke is capable of doing things with the force, and then once at the end, again under Obi Wan's (posthumous) tutelage, in the climax of an entire film where Luke's learning to use the force has been a major subplot, arguably even the driving force (pardon the pun) behind the plot as a whole. And that ignores all the other indications throughout the film that the force is incredibly powerful, and capable of doing amazing things. Again, it spends time during the film explaining a concept, then that setup makes a climactic action scene make sense. Forget the EU, or the rules of the SW universe, or any of that. This is filmmaking 101 - hell, this is storytelling 101. Set it up, then pay it off.
Compare that with Rey. She gets into and flies the Millennium Falcon without any set up that she's capable of piloting any kind of ship at all, let alone that specific type of ship or whatever. Yeah, she drags it across the sand, implying that she's not a very good pilot - which is fine. No set up, no real pay off. But then, pretty much out of nowhere, she flies it through the hulk of the Star Destroyer and pirouettes it into a perfect position for Finn to eliminate the pursuing TIE. Now, you can come up with after the fact justifications for her ability to go from dragging the Falcon through the sand to incredible precision flying in a minute or two (and people have in this thread), but the film itself never delivers them, and it certainly didn't deliver them in advance. Sure, maybe it'll be explained in Episode 8, but as a standalone film - and that's all we can judge it as right now (at least, as far as Rey as a character goes), it fails in this regard.
It's the same for the repairs on the Falcon - we never see her repairing anything, or hear anyone say she's good at it. Maybe as a scavenger she has some aptitude, but we never see it on screen until she can suddenly do it at a clutch moment. Same story with the force. Yes, at a meta level we knew she would turn out to be strong with the force, and yes there was the scene with the sabre and some vague set up from Maz Kanata, but within the film itself, the set up was minimal, and the payoff was huge - she mind tricks a stormtrooper with no onscreen evidence that that was even possible, beats Kylo Ren (the film's big bad, and someone we have on screen evidence for being very strong with the force) at telekinesis - again, something she'd never been introduced to - then beats him in a lightsabre fight with no training.
Again, yes, you can justify these after the fact f you want to, but it remains that Rey demonstrated advanced competence in three specific skills at precisely the right, critical moment to save the day with no or very little foreshadowing. 1 is maybe forgivable, depending on the specific ability (fixing the falcon for example, would be more forgivable than being an unexplained force savant), two is bad storytelling, but three is fanfic-author-insert levels of unexplained awesomeness and bad storytelling, even if she maybe doesn't fit the textbook definition of a Mary Sue.
