It's true, the lives of the soldiers on BSG aren't what they would have been without the apocalypse and exodus. Some would have retired, or been assigned to another ship, etc, but these are people who were living on a battlestar both before and after the attack. Their lives were put into stasis, not a new post-apocalyptic series of crises. It's true, their lives are more strenuous and stressful than before, but this could have been the result of traditional space war. By focusing on the military life, BSG looks at people whose only change is a lack of any possibilities for advancement.
So what would be different for the society and civilians in BSG? Property, trade, industry, and money would be shattered. There is no traditional police force, and the military doesn't have the time, ability, or interest to resolve contests of ownership between civilians on another ship. Once people realized that the state as they had known it was extinct, all property would be up for grabs, and control of ships would be a literally a matter of life or death. The passengers of a transport may not have been concerned about the ship's commander for their two-day trip, but once they realize that this ship is going to be their home for a long time, a new form of ship's governance would be almost inevitable.
Unless the "federal" government run by the President managed to install a police force loyal only to it on each ship, each ship would essentially turn into its own government. The ships would be forced to follow the fleet, as following the Galactica is the only safe path, but the internal functioning of each ship would necessarily fall to the impromptu governments that would have to take shape on each ship*.
Industry is a point that BSG has never even addressed, at least as far as I am in the show. Everyone just has new stuff all the time, even though all the factories in the universe got blown up over two years ago. I sincerely doubt that the few ships in the fleet carried the facilities necessary to create and process plastics, forge new metals, armaments, and ammunition, and so on. This would mean that manufacturing would have to be improvised, and scarcity of everything would be the norm. Even simple things like clothing would wear out and need to be replaced, and even if that pleasure ship had some cotton bearing plants, it wouldn't be nearly enough to clothe hundreds of thousands of people. Trying to make a new industrial economy in a space fleet would be terribly interesting.
At one point, Tom Zerik points out that their money is now just paper, a meaningless symbol from their previous lives. It's true that money from before the exodus would have to be re-evaluated, but it could easily become the new currency of the fleet. Money is necessary in most any society that cannot operate between a few hundred people with resources whose value is fairly well understood. After the exodus though, a lot of people that thought of themselves as "rich" or "poor" would find a new reality. Suddenly, all those credits they had in a bank that no longer exist mean nothing, and possession of a firearm can make you king of a small ship without organization. The "sorting out" of a new fleet society could have been a great plot. For a brief time, each person could remake themselves, before the inevitable calcifying of a society in a small population.
Early in the show, the president points out that people "have to start having babies". This is true. Of course people do that naturally, so she doesn't have to make anyone do it, but I think she should have gone further to encourage breeding.
- It would be bad for the show, but any reasonable person in BSG wouldn't allow women to be involved in dangerous tasks, and especially be exposed to radiation, unless there is some form of artificial womb in BSG**. Women are the bottleneck in increasing the human population, and should be encouraged to have as many as possible with as large a variety of people as possible.
- Why a variety of people? Genetic diversity. If only one or two people carry a gene in BSG, it would be very easy for that gene to go extinct. A reasonable society would at least harvest a "DNA sample" from every human being in the fleet.
- Remember that episode where the president banned abortion, but allowed the girl in question to do it anyway? That was a weird series of decisions. Anyway, under the same logic of "humans need to breed, ergo we can't allow abortion," she would be a hypocrite to not bar contraception.
- There's an interesting sociological question embedded in all this: would people be more or less eager to have children in this post-exodus world? There are factors that point in both directions. After a crisis, people like to have kids. When there are fewer people, there is a natural instinct to make more of them. But reasoning people would have to look around the crowded halls of their ships, the bare cots that constitute their homes, and wonder if it was a good idea to bring a new soul in to this bleak new world.
Well, this isn't all I had to say, but it's long enough.
*This would have made for a more interesting show, I think. Imagine the federal government trying to force one of the ships to follow some law that they weren't interested in. What sort of negotiations might occur? What forms of government might each ship take? Could a democracy somehow form on a ship with only a couple hundred people, and survive despite all the stresses and tough choices that such a government would have to make? How could a democratic ship negotiate with another ship with a charismatic captain/dictator like Admiral Adama?
** Unlikely, given their level of technology throughout. I love the show's decision to have technology inferior to our modern technology. The show can never be made obsolete! Great idea.