Ok Just got back from seeing it the second time and a few more things I noticed since I wasn't geeking the fuck out.
1) At the start when Finn wakes up on Jakku, you can very clearly see his seat ejected with a parachute. Since when did the Empire/FO care of about Tie Pilots to the point of giving them parachuted ejection seats? Most TIE's didn't even have shield for the very reason that the pilots were a dime a dozen. Maybe since the defeat things have changed.
2) Mox Van Sydows Character has way way more backstory we are not getting, he Knew Luke, knew of the Solo's, Knew Kylo's identity and obviously fought in some capacity in the war along with the Jedi. I am really curious who he ends up being.
3)When Kylo knocks Rey out in the forest, she is holding the GUN han gave her down at her side, so it is assumed when she is knocked unconscious she drops it, but we later see her with the exact same gun at the end of the movie. Small error there, but nothing big.
Regarding Rey's Powers
Ok my main theory at this point is that When Kylo Mind rapes her, they essentially exchange information. He learns about the BB droid, the island and her dreams. And she SEE's into his mind learning about his Vader obsession and other things along with what I predict is memories of Kylo using the force in various ways and more about the essence of the force from him. He essentially "awakens" her latent force abilities when they have the Mind Orgy and grants her some rudimentary knowledge on how to use it.
He even comments on this in the movie right after she escapes when he says "She is just beginning to tap into her power, the longer she is free the more powerful she will become" or something along those lines, and I think between that and he "letting" in the force as per Maz Kanata she becomes strong fast. Also keep in mind that the Lightsaber she holds is a powerful relic with a strong imbuement of the force so her "believing" in the force on top of having it awoken in her by kylo + holding the skywalker force relic opens her up to the force. And we all know as per ANH the force "guides your actions".
DO I think it could have been explained better? Sure but I think there is enough there for it to make sense. Also after re-watching you see how fucking powerful the bowcaster is and realize that kylo is in serious hurt. Finally for those saying Finn held his own. Your REALLY need to rewatch it. He gets owned super fast. Kylo basically dodges all his strikes and Finn is falling backwards the entire time. He only gets the lucky shot in because Kylo is very rough and unchecked and is swinging wildy in anger thus causing him to be very open for the small hit he takes back.