I like Rey. But I'm also a writer so it's handy to think about character growth and Mary Sueishness of characters.
Here's a test:
I don't know Star Wars well enough to answer for Leia, Luke, Han or Rey (But Anakin scores points for being a slave). Mary Sueing isn't just about being competent as all these characters are good at something on day one.
The usual goal for main characters (as a writer) is that they have a change and growth arc. They make mistakes. Does Leia? I'm not so sure. She's largely composed and competent in ANH. Falls in love with Han in ESB. Kicks butt in ROJ. I sense that she might not be a main character. Which means she kinda got hosed on story (assuming every character's meta-goal is camera time emoting and evolving their character).
(here's a link on character arc from an expert writer advice person so we're all on the same page)
The Character Arc in Six Specific Stages
Luke starts as whiny, always in a hurry to get to out there, never focused on where - he - is. At the end, he's calm, he's collected, and he's ready to confront and turn Vader. A very definitive character growth arc where Luke is not the same person. Almost like Lucas had read a book on the subject...
Does Rey have any flaws? Poe does. Finn does. Their faults are very obvious conflict and growth points (or in Poe's case his flaw is a strength)
She does have those flashbacks and questions about where she came from, being abandoned.
Aside from improved Force skill, does Rey change in any way? She's strong, confident. Does she ever do the wrong thing? Whether she's a full Mary Sue or not, there's signs that she's not getting the full Arc treatment.
Do we ever tackle that abandonment issue? Does it ever come up or hold Rey back?
this might even be a side effect of being a major female character and the writers trying to make her a role model or avoid negative connotations about her flaws if she had them. I still like her, but it'd be an unfortunate loss for her. But I wouldn't panic over it. I still like her character.
We all like Ellen Ripley, but does she really have a change arc? The whole story is "nobody listened to the woman, so they all died except for her and the cat." I doubt Mace Windu had much of a change arc, but he was a bad mutha-jedi. Oh wait, the story wasn't about Mace. Funny that. Is it possible that the story's not about Rey? That she's really a catalyst for Finn, Poe, Kylo and Luke?
From the standard of the old serials (of which Star Wars is an homage), character change/growth didn't really exist as most of the focus was on external issues (saving the princess, earth, dog, etc). So as George says, it's all popcorn.