First off, the movie was a lot of fun to watch. Just the right mix of action, suspense, humor, etc. What's better, is that between this and the TV show, I really, truly care about these characters and what happens to them. So the rest of this may sound critical, but it just goes to show how much these characters have gotten to me.
I'm royally ticked off that they killed Wash. Less so about Shepherd Book. I think what hurts the worst about both is that both deaths were out of the blue; it felt like they were only done to shock the audience. ("See, we're serious! People die!") If this were a Marvel comic, I wouldn't be as ticked, because it can always be undone. But in a setting without magic or insta-cloning & brain transplants, it just isn't going to happen. Taking a step back to think about it, however, I think I can guess why Joss went that direction. Book was essentially expendable; he was there to be a moral anchor or conscience, and to be a source of mystery. The mystery is basically answered now, I think, and Inara, Kaylee, and to a lesser extent, Mal, can otherwise fill the conscience role. As for Wash, now that River is apparently sane and the Alliance likely aren't actively hunting her, she needs a role on the ship; without it, there's not really any real reason for her to stay. If she went or died, Simon would likely follow or leave; and if he left, Kaylee would likely follow; that would gut the cast probably beyond repair. Wash's main role as a character was to crack jokes, swear in Chinese, and to fly the ship while the others ran missions. With Wash dead, River can become the navigator and have a purpose on the ship. Zoe's first loyalties have always been to Mal, so she'll be extra moody most of the time, but she'll stick by his side. (I don't think her history with Mal was made as clear in the movie as it could have been for those who haven't seen the TV episodes, but they couldn't include everything.)
The more I think about the Reavers, however, particularly with what is revealed in the movie about their origins, the less sense they make for me. If they're that mindlessly violent, how on Earth do they have enough of a society to fly a spaceship? Given that they've been out there for more than a decade now, most of the time in close proximity to each other, why haven't they wiped each other out by now? And if they're really that much of a risk to the civilized planets and their origins are that much of an "embarrassment" to the Alliance, in all the time since then (and particularly any time in the recent history), why hasn't the Alliance tasked a small fraction of the task force that's been hounding the Tams to wipe out the Reavers (particularly given how clustered they are in front of that planet)? Alternatively, given the Alliance's inability to prevent the Reavers from raiding the outer planets at will, why haven't the outer planets raised holy hell about that fact? The Reavers obviously fill the niche of the Indians in this "space western" (except they're mindlessly violent, so that there's no taking their side), and in the real West, keeping populations safe from Indian attack and waging war against the Indians was one of the main duties of the Army. They didn't win every battle (q.v. Little Bighorn), but they were constantly pushing the Indians further and further back. And after the Civil War was over (Serenity's Alliance vs. Browncoats), it didn't take long for the U.S. to send its quick-strike forces (chiefly the cavalry) that direction.
Also, I don't really buy River's new-found sanity. Was the dead planet really the only secret that's been burning a hole in her mind, so much so that finding that recording was enough to cure her of her psychoses, leaving her sane and reliable (if still psychic)? And while I can see why the Alliance might broadcast a subliminal message that would trigger her (in order to make her presense obvious), why would that trigger her memory of this planet--wouldn't that be the last thing the Alliance wants to have happen?
Out in the realm of nitpicking, "Mr. Universe" strikes me as a retcon and a handy macguffin. If Mal was on such good terms with such a character, why didn't he take advantage of that sort of connection back in the TV series? The character & his lair seem to exist only to give Our Heroes an easy way to achieve their end. I also wasn't aware that all of the stories took place in a single solar system; given that, how could "Out of Gas" take place in an area that's completely off the shipping lanes, but is still a viable route between two planets? As the planets revolve around the sun, the shipping lanes would likewise constantly shift! (So a spot might be off today's shipping lanes, and might be off of them for long enough that help won't come anytime soon, but it'll be on the shipping lanes eventually.) Also, if the planets are far enough out that it takes a long, long time to revolve around their sun, how in the world is there room for that many planets in the habitable zone around the sun (even assuming that a lot of them are moons of larger planets)? If that many planets are somehow crammed into the habitable band around the sun (evenly spaced in each planetary orbit's Trojan points, for example--lots of moons in Trojan lunar orbits are less likely, given other in-show evidence, as then there would be quite a bit more travel from one to the next, and from that set to the next higher/lower orbit around that planet), then that just increases the chances that there'll a nearby shipping lane soon. Again, not in time for anyone to come to the rescue, but still one of the inherent problems in setting everything in a single solar system and then claiming there are areas between planets where no spaceships ever go.
Feudalism: Serf & Turf