Cut? More like saved for further stories.
Yeah. I misspoke about backstory. I was thinking backstory because I was thinking of Nero. I'd say Rey's Force ability, her parentage and why she was left on Jakku being sequel fuel is more than fine because it will motivate her development through VIII and IX.
I feel some of Rey's Jakku scenes got cut, and that leaves what is left to explain why she can do certain things so well, kind of flimsy. Even with stretchy, single-line explanation, Star Wars-logic.
My main contention was her being a great pilot. For some reason, "Finn - Where's the pilot? Rey - We've got one" doesn't really work as well for me as T-16 womp rat Beggar's Canyon does. I understand the circumstances of those scenes were completely different, but VII's version doesn't fill that logical gap like IV's version did.
Rey fucking up the lift-off doesn't handwave her being able to drift and pull post-stall maneuvers in what effectively is a space truck. Star Wars-logic only stretches so far.
One could say the movie is trying to infer that Rey flew quadjumpers for Unkar Plutt, but I feel that's so much of a stretch that it falls into head-canon.
I heard they cut a bit where Rey was using a flight simulator at her condo, which I think would have been cool to see. That plus the exchange with Finn would have done okay with me.
Rey knowing her way her around the Millennium Falcon so well is, at most, a minor nitpick. It's noticeable, but only if you think about it and it doesn't really subtract from the experience. Her being a part scavenger + working for Unkar Plutt is enough explanation for her technical skill. The Millennium Falcon being there was set up as a surprise for SW nerds. That's fine.
Rey being able to deadeye Stormtroopers the first time with a blaster - that's fine. Star Wars does that shit all the time. The good guys can hit anything and the bad guys can't hit shit.
Rey being able to hold her own against a weakened Kylo Ren is explained by her fight with the thugs in the market + Kylo Ren was weakened and unfocused and he didn't want to kill her + The Light Side Of The Force + sequel bait.