(Mostly minor spoilers)

I hadn’t heard of a Mary Sue when I left the theater thinking too much of the movie was cheap. (Though I enjoyed it, perhaps a tad more than you, Mav.) You’re right to say that some people want flawed but compelling characters who develop and didn’t find that in Rey. That’s probably why I liked Kylo Ren better. (Btw, it’s weird people are saying he’s not a very good Jedi, in order to make Rey’s victory more in order. When you first see him, he stops a blaster bolt in mid air and then leave it there interminably without paying it any mind. His issues aren’t that he’s a bad Jedi.) But I didn’t think she was too perfect. On the Falcon, I figured an experienced scavenger would have to have a reasonable knowledge of how a random ship works. Instead, I blamed Abrams for taking shortcuts to fit in too much movie. The shaking lightsaber calls back to Luke’s process of mastery, but doesn’t show a process. It’s shorthand. Maybe an actual training sequence would be too boring in a reboot, but that’s not really an excuse. Like you say, it also has to stand on its own.

–actual spoiler here–
When she tricks the stormtrooper, that was particularly awkward. What she learns in two failed attempts was that she needed only try a little bit harder, as if it were being played for laughs despite being an important plot point.
–end actual spoiler–

She doesn’t feel like the main character. (It’s possible I’m being sexist, ignoring her, and then wondering why there’s no true main character. But I think it’s because she doesn’t develop.) You point out how Luke’s training was pretty short. (In my memory, it certainly feels a lot longer, as if Dagobah were a training montage with the same rules of condensed time.) But also, as you also point out, Luke fails repeatedly. The limits to his training limit him, and by the contrapositive his training is important. It’s possible he might fail, because he repeatedly does. Possible at least in the sense that failure of a truly meaningful sort is never really possible in a movie, but there’s tension there. The only tension I found in The Force Awakens came from wondering when, how, or even if the film will deviate from A New Hope. That was kind of fun, but it won’t stick with me.