Star Wars:
Mostly see everybody else for spoiler thoughts. I should add that I went in almost totally blind - as in, I didn't see any trailers or ads.
Direct sequels involving the main cast (i.e. not side stories which have a lot more leeway) are always tricky, as there's two options:
A) Don't rock the boat, don't change the characters, don't undo anything they've accomplished before except perhaps in an obviously fixable way. This has the not inconsiderable benefit of not retroactively screwing up earlier stories, but usually makes things too safe & predictable.
B) Be daring, mess stuff up. High risk, high reward.
On the continuum, you probably need to go B for a compelling story. Sadly, the downside is real here, and the same as the EU: introducing new crises diminishes the triumph in Return of the Jedi. Even worse, you have to do things like say "No, Han & Leia did not live happily ever after, and Han apparently became some kind of failure to explain why he's still wheeling & dealing rather than being a high muckety-muck." It is the right choice for this movie, but it's a painful one for the series. Oh well.
I agree that adding some kind of throwaway line, or something in the opening scrawl, to make more clear what exactly the relationship between the "Resistance" and the Republic was. I think that the writers think - somewhat correctly - that there's some ill will toward the "servants of the Republic" setup that was in the prequels. So they were desperate to cast the action is being headed by a scrappy Resistance and wanted to spend 0 time elaborating on what exactly their link to the Republic was. Suikoden V had a bit of a similar thing, as the game desperately wanted to insist that you, the friggin' Prince & Royal Aunt, were leading some kind of heroic rebellion rather than presenting your forces as the legitimate government dealing with traitors. I do hope that after the success of this film, they're willing to edge a bit back into talking about the Republic.
On a related note. Starkiller Base. So... it can shoot other star systems if I understand correctly? This seems a little too godlike in power, Star Wars has been well-established that its super-weapons conveniently need to get into attack angles, take time to power up, etc. for good & proper dramatic reasons. And blowing up the Senate wasn't really established well, unlike Alderaan. Yes, I get that they wanted to hit the exact same notes as the Death Star, and that means amping up the stakes, but bah. Building something like this would also take ages, so not noticing was a supreme failure on the Resistance's spies, but that's how things roll in movies I guess. Additionally... if this is a converted planet, did they really have to blow the whole thing up? I'm sure that there'll be some excuse that they actually converted a planet with no sentient life on it or something, so it was just First Order lackeys on it, but still. This would get REALLY dark if they had to destroy a planet to save others. Then again, as others have pointed out, this movie explicitly struck back against the "Stormtroopers are disposable clones you can slaughter without feeling bad about it" meme that the prequels tried to set up, so maybe they really are willing to go there.
I like the new cast a lot. One benefit of going in totally blind was that I was willing to believe that Poe Damaron might actually be dead, but sure, he's fun so I'm glad he isn't. Rey & Finn both seem like they have interesting plot arcs ahead of them, and BB-8 is super-cute, which is a niche not taken by a droid yet.
As another thing the writers explicitly borrowed from Star Wars episode 4, I see that everybody is back to thinking of the Jedi as myths again. I guess people lap this stuff up, buuut it's really not all that credible. The Rebel Alliance all said "May the Force be with you" & stuff, you'd think they could have imposed their theocracy on the New Republic. People generally want to believe in a religion, after all, especially one that says you'll become a Force ghost and help your friends if you die!
Anakin/Luke's lightsaber should totally have been disintegrated in the middle of Bespin, or whatever the gas giant the cloud city orbited was called. But I guess maybe it just got stuck on something and some poor janitor droid cleaned it up from the bottom of the pit in the worst job in the world. Ah well, nitpicking.
Speaking of which, leaving Luke largely out was totally the right call. He'd dominate the action far too much. Part of why making the sequel at all is a bit disspiriting that he NEEDS to be at least temporarily out of commission, or immediately killed off a la Ben Kenobi, and keeping him isolated was probably the right call. Dunno why Snoke particularly cares, though.
Speaking of which, I really hope that Snoke isn't somebody possessed by the Emperor's dark spirit or something, a plot twist the EU allegedly used a bunch. Also, I knew enough about the EU to assume that Rey was a sister to Kylo Ren as well, but I'm convinced that the odds are more likely she's Luke's kid at this point, even if the sister angle is possible. If they play the sister angle, it'll have to be something like "our daughter TOTALLY DIED in Kylo Ren's betrayal somehow, so this can't possibly be her!" Cousin is probably more workable, sure.