WARNING: Spoiler for the first minute of the Serenity movie.
One of the big questions about Firefly, at least for nerdy types like me, was "Can Serenity travel faster than light?" Seventy (or more) Earth-like planets normally take up a lot of interstellar real estate, but there wasn't any indication of FTL travel in Firefly. One hypothesis that came up on the boards (and I have no idea who first proposed it) was that the setting was a large solar system centered on a blue star. For the non-astrophysicists, that's a very big, very bright star which would have a much larger area where planets would receive Earth-like levels of radiation, so there'd be room for many useful planets to orbit around it. This would also explain the Blue Sun corporation's name--it's the big star that everybody else revolves around.
There's a few problems with this, though. Planets are spaced far enough apart that even a blue star would only have one or two in the habitable zone. That's assuming it does have planets--some theorists think the intense radiation from the star would blow away dust and gas before it could condense into planets. So you're way short of the seventy new Earths Mal mentioned.
But Serenity settles the question right in the first minute by saying humanity relocated to a blue star system. So how the heck did it get so many planets?
Poul Anderson set a story on a group of planets around a blue star. His scenario was that some fully formed rogue planets (ie, planets formed away from any star) wandered into the newly formed blue star's gravity well, were slowed into orbit around the star by drag from the surrounding nebula, and assumed their final orbits as the newly ignited star blew the nebula away. The timing on that is incredibly narrow though. Anderson was only willing to suppose a half dozen planets in the habitable zone even with that unlikely coincidence.
Now we can broaden the definition of "habitable zone" with terraforming methods. Planets close in to the sun could have a thick cloud layer established to reflect away as much light as possible (this matches Wash's description of his homeworld). Outer planets could have dark lichen or plankton covering the surface to absorb energy. Moons of gas giants can also be warmed by their primaries--a superjovian planet can put out enough heat to let a colony survive outside the nominal habitable zone. But that's still not going to get us seventy worlds.
So what's going on? Could be the 'verse has a natural accumulation of planets around a blue star. That trashes hell out of the current planetary formation theories, but those have been coming apart anyway as more extrasolar planets are discovered (they're not matching the old theories at all). In some SF settings it'd be perfectly reasonable to assume that some old alien race had arranged the planets for their own reasons and then died out, but the Firefly 'verse is alien-free and it'd be nice to keep it that way. Possibly another star had a close approach and lost its planets to the blue star, but that'd be hard to arrange, and you still wouldn't get up to seventy, because a 2nd pass like that would trash most of the planets from the first encounter.
So how else could it happen? Well, some of the technology we've seen in the Firefly 'verse is cheap contragravity and safe cold-sleep. Cold-sleep was essential for evacuating Earth. Most of the population probably stayed in storage until a planet was prepared for them to land on. It also allows a terraforming crew to start some process going, then step out for ten years until it's time to do the next step.
But the contragravity tech could scale up. We haven't seen any terraforming ships, but the Alliance cruiser is huge. Presumably an even bigger tug could be built. Or they might have some big ships lying around--the motherships which hauled a good chunk of the human race many lightyears in just a century or two, sublight. That's going to be a *huge* ship with *very* *powerful* engines. Something like that could nudge a small planet into a new, more usable orbit. Sure, it'll take decades, but what's your rush? The population is still frozen, dumped in some nice parking orbit. The terraforming crew can freeze out for a few more years until it's time for the next maneuver, or move on to the next planet.
Once we have them in a good orbit they need air and water, but smashing a few comets into them will supply that. The really hard part is getting Earth-normal gravity on them. I figured this wasn't really possible, and we'd just have to handwave the show having 1.0g for every planet,
EDIT: Oops. Gerry Tyra has pointed out that neutronium is only stable under pressure. So unless there's some way to use contragravity to crush silicon and iron into heavier elements such as mercury, as soon as you release the pressure from a planet you're crushing it'll spring back to its original size. With a noticable energy release. So that leaves us playing billard balls with planets and asteroids to merge them until they're big enough to have acceptable gravity. You'd still have some crushing work going on to round out the merged mass--wait for gravity to settle it would take too long. That won't get us to exactly 1.0g, though. But anything close to that should be tolerable.
That's the heavy-industry part of the job. It leaves you an utterly uninhabitable world--the atmostphere has no free oxygen, there's no plants growing, and the crust is unstable. But that's when you bring in your expendable-labor terraforming crews. They do the detail work of spreading plants over the whole surface. Dangerous work. Which is why the slaver ship captain was making such profit bringing in replacements in Ariel. Hard labor, breath mask accidents, frequent earthquakes--lots of replacements.
But in the end they'll have dozens of habitable worlds, bringing on another every few years. That can explain some of the different numbers--you'll get different ones depending on whether you count ones open for colonization or just reaching its target orbit.
So I think I can buy Whedon's setting after all. The key assumption--big ships with powerful contragravity drives--fits with the opening scenario. The final stage matches what we saw in the episodes. And Joss can tell the difference between SF and fantasy.