I do agree that, in some ways, it's a little bit of a turn-off that the story is, virtually scene for scene, Episode IV all over again, but I also can understand the way it's used for set-up for the next generation of characters.
I'd say my biggest complaints would be...(and, of course, these are solely contained to Episode VII itself, so please don't give me "maybe (complaint in question) will happen/be answered/be shown/etc. in the next movie(s)" replies as I already know it's a good possibility =) . Also, these are obviously not deal breakers because of such possibilities, so some can be as little as nitpicks too, lol)
A.) Lack of explanation for where the First Order came from and how they could rise to such power without being quickly detected and snuffed out by the New Republic (which we also don't see anything of; only mentioned a couple times), especially when you consider they built a super weapon that was practically five or more times bigger and far more threatening than the first Death Star (only the Death Star II has an edge with its super laser charge time of merely a few minutes, despite the Starkiller Base being able to wipe out several planets with a single shot). I'm also pretty sure they won't want to make another political-based trilogy to explain such a thing considering the hate towards Episodes I, II, and III (though, IMO, I don't think they're as bad as people say. Certainly not great, but not the worst things ever either.).
B.) Lack of other starfighters besides the X-Wing and TIE Fighter (though the TIE Fighter was at least improved with a rear gunner and extra weapons the originals never had). You'd think we'd see the Y-Wing, A-Wing, and/or B-Wing flying around as well as (improved) TIE Interceptors, TIE Bombers, and whatnot. We wouldn't need all of them, of course, but at least seeing Y-Wings or A-Wings alongside the X-Wings to fight the TIE Fighters and/or go after Starkiller Base like Episode IV had Y-Wings with the X-Wings.
C.) The use of Captain Phasma. They make her look like a total badass in the trailers and such and you'd hope she'd be one of those awesome sub-boss type characters that the cast needs to overcome in a difficult battle (like what we'd want with Boba Fett), but instead, she barely has any lines, barely has any appearances, and her only big appearance is largely just being used as a way to push events forward and as Episode IV homage comic relief.
D.) As it was mentioned, the way Han Solo's death is just sort of glossed over after the fact. As such a legendary figure to the new generation and such an icon to the Republic/Resistance in general, you'd think there would have been some big, if brief, funeral before having Rey take off to where Luke was.
E.) Anakin's lightsaber. How was anyone able to find it after Luke lost it on Bespin in Episode V after Vader cut his hand off? Such a tiny object falling down such a huge shaft (who knows where it lead?) makes it hard to believe it was recoverable. If it was Luke's own green lightsaber that he himself constructed, it would have been more understandable.
F.) Also as was mentioned, Rey seeming to just be able to use The Force without any sort of prior training or experience. Even Luke had to have some training by Obi-Wan before he could do things like calling Anakin's lightsaber to him like at the start of Episode V (and even that took effort on his part) and then being in a bit of seclusion between Episodes V and VI, resulting in such a dramatic change from the end of V to the beginning of VI, and even Kylo Ren/Ben Solo required training from Luke and Snoke.
G.) Kylo Ren's obsession with Darth Vader and what exactly Vader "started" that he intended to finish considering, if it was the general thinking of the Dark Side winning, than you'd think he'd be obsessed with Palpatine rather than Vader as Palpatine was the one who brought up the Empire and all, so it makes me think there could have been something else going on before Vader returned to being Anakin and died.