Well, let's see... This probably doesn't mesh with the map in the movie, but if I wanted to have a dozen planets and a hundred moons in the habitable zone, and I had terraforming capability that included gravity adjustment...
OK, let's assume the habitable zone, with terraforming, extends from about the orbit of Venus to about the orbit of Jupiter. (Using some greenhouse effect to maintain heat, and maybe orbiting solar mirrors to increase the amount of sunlight hitting the planet.)
I just used an orbital simulator to simulate nine planets varying from Mars to Earth mass at orbits 20 million kilometers apart, starting at 100 million kilometers from the sun. It looks like the orbits are pretty stable, at least over a thousand years. The simulator only allows for ten objects, but 20 million km separation of orbits would allow for twelve habitable planets between 100 million and 320 million km from the sun, which works.
The moons are more difficult to account for, but if we assume some of them are just asteroids put into orbit around some of the habitable planets, then I think it could work.