And that's the problem. There was no growth.
I know she is mechanically inclined, but being able to fix a ship isn't the same thing as flying a ship. There are mechanics who are horrible drivers.
I'd say the problem was that there was no training. Rey went from being a garbage picker straight to being a high-power padawan. And I don't think being a garbage picker makes you a culinary genius either. I never saw any technical manuals in how to repair ships in Rey's room. The only thing we ever get to see her actually fix is BB-8's bent antenna. All we really see is that she pulls random parts out of crashed vehicles and that she brings them to a guy who gives her food in trade for them. She is never shown to be any sort of mechanic. She is never shown to know what the parts she pulls out of wreckage are, nor what purpose they served. She's shown picking parts, cleaning parts, and trading those parts for food.
Please don't misuderstand me, I like Rey. I don't need Kristen or anyone else popping in to say I'm a Rey-hater or anything.

(And yes I say that with great trepidation in that it may be taken the wrong way, I'm not trying to poke the bear so to speak, I just know how much she loves Rey and I don't want to get too far without saying I like her too and accidentally have everyone trying to Force-choke me because they think I don't). I just don't like how Rey's story is, or rather isn't, presented to us. Strip away the Force stuff and the unexplained mechanical genius and we're left with a character with a full range of emotions, who is both endearing and inspiring in her spirit.
I guess I care less about the amount of power they're giving her, than the fact that she all of a sudden knows how to use that power. It would have been more believable had she been in a dramatic situation where she cried out "STOP!" and everyone around her froze. Or if she'd thrown her arms out in a reflexive catching motion to someone falling and cried out "NO!" and she kept them from hitting the ground. She would have been able to put the two together in either case and learned from those types of scenarios. But no, she tells the guard to let her go, THINKING that it'll work. Who taught her that? Did she magically glean it out of her incounter with Kylo Ren when he was trying to Force-pry the map out of her thoughts? Was that from some story about Jedi-mind-tricks that she'd heard growing up? Then tell us in the story that that's how she figured it out! Without any lightsaber training she should have been chopped to pieces in the lightsaber duel with Kylo Ren. Did she magically glean all that knowledge too? I can give Finn a pass on surviving his encounter with Kylo in that we had already found out that Stormtroopers have a new anti-lightsaber weapon and have been trained to battle against lightsabers. One of the two Stormtrooper cadets would have used a lightsaber (or some sort of shinai/bokken stand-in / Obi-Wan's hut back-scratcher thingy) during that sort of training and they would have swapped back and forth who used what. But was Kylo really only trying to scratch Finn? I know... that's a different discussion. Where was I...
It's called The Force Awakens.
Yes, but it isn't called 'You are now a Jedi".
He literally hasn't changed, he's still the same person. Yet no one complains about him. What's the difference?
Captain America was given a serum to increase his physical abilities. He already knew how to run, now he can run faster. He already knew how to jump, now he can jump higher. He already knew how to duck, now he can duck faster. He already knew how to jump off of something, now he can survive jumping off incredibly high objects. He already knew how to fight (even as a scrawny dude, and even though he often lost, and like you said, he fights for what he believes in); now after the serum he has the ability to win because he's stronger. The serum didn't magically teach him how to do all of those things, it made him more capable of doing them.
Rey was given powers that are growing faster than she realizes. The more time that passes, the stronger she becomes and the more she learns about her powers. But there isn't much there to say how she's learning about them. And there's no explination as to why they're becoming stronger. Luke could only grow in his abilities by straining to use them. Luke could only become one with the Force when he was calm. And Luke was being taught not only how to connect with and use the Force, but also how to use a Jedi's weapon. Rey's being chased around and exponentially growing in the Force with no one teaching her anything... sounds like the quicker, easier path to me. But if she was being seduced by the Dark Side, there's no explanation of that either! So the difference is that Rey doesn't know what fuses do what... O.K. she still doesn't, bad example.

Rey doesn't know how to fix spaceships, yet now she can. Rey doesn't know how to resist a Force-probe, yet now she can. Rey doesn't know how to Jedi-mind-trick people, yet now she can. Rey doesn't know how to Force-pull a lightsaber to her, yet now she can. Rey doesn't know how to duel with a lightsaber, yet now she can. In short Rey don't know. And now she can. Magically.
I wish her story had been told more thoroughly, more coherently, and without all the giant leaps that we're just supposed to absorb without explanation.
If it turns out Rey really is a nobody, I wish they'd have made her a separate story, and not a part of the Skywalker storyline. The sequel trilogy should have been about Luke rebuilding the Jedi, the new Ben should have been a Skywalker, Daisy Ridley should have been Jaina Solo, Adam Driver should have been Jacen Solo, and we should have had a FORCE TON of Grand Admiral Thrawn. Oh yeah, not to mention we could have had another kick-@ $ $ female character... Mara Jade anyone? How'd the S.T. get so messed up?!?!?!?!?!
That way Han wouldn't have been killed off by his son, Leia wouldn't have become Mary Poppins, Luke wouldn't have been Rianed, and to bring this back on topic... nobody would have torn the GRAFLEX lightsaber in half!