In a recent episode of Stargate Universe, we learn that alternate versions of the crew ended up back in time stranded on a planet. They proceed to establish a colony, which over the years grows to a massive population of millions. Is this even possible? Do they have a large enough group of people that they wouldn't end up too small a gene pool for a healthy population to grow? This says that at the start of the show they had roughly 80 crew, which has shrunk a bit due to miscellaneous deaths. I had similar issues with the recent BSG and Voyager, but both shows resolved that issue in the end.
Well, the founder effect implies that they would most likely end up with lots of genetic defects coming from a population smaller than about 200, but with careful breeding charts and mandatory non-monogamy (to ensure maximum diversity of genes no individual male could have more than one child with any single female), it could be possible to rebound from such a tiny gene pool, but the sociological changes needed to survive would probably be too great to bear.
Uhm, I have to say they would probably suffer some of the negatives of inbreeding over time, but I doubt it would be enough to actually significantly affect the health of the offspring. I mean they start with under 80 people, but those 80 form a pretty diverse genetic pool (it's racially diverse and they don't seem to have any family groupings onboard). Assuming they carefully watched the family lines they could probably eventually make it to a large enough population to breed safely.
The depiction of the early years seems alittle far fetched to me though. They ofcourse start technological reconstruction with something of a head start, but it doesn't strike me that they would have the skill set or the resources to advance as fast as they're shown to have done. Also a very large part of their knowledge would pretty much have been completely lost when the founding fathers died off. Let me put it another way, when you're 40 years old have to figure out a complete new social system, deal with internal strife, and try to figure out how to survive on a strange planet (including figuring out crude ways to harvest resources like timber and iron) it doesn't leave you much time to explain even the basics of nuclear physics to your children, children in whose lifetime that knowledge will have zero application and who even if they do learn it will be unlikely to pass on that knowledge to their own children or grandchildren.
I'm not certain how long these people are supposed to have lived on that planet, but their society and speech also seems to have undergone very little change or development. Just consider the development of the English language in the last 20-30 years and you'll see it's pretty ridiculous to expect them to be speaking the exact same language after so many generations.
To sum it up, I think with some work, and given time it's plausible they could build such a population even with such a limited genetic pool. That that population would show such a remarkably static social structure and maintain the english language for so long, seems are little far fetched.
The population issue shouldn't even be an issue. They've had 2000 years to make a population of millions. Consider even the Earth's population, from the year 0 to the year 2000, we've had a huge population spike. Yes, we started with a lot more in 0 than just 80, but we're currently in the billions (though not yet a Sagan).
And, like Tangurena said, the genetic defects could be overcome with mandatory non-monogamy, and technically even without mandatory non-monogamy, so long as there was a clearly recorded genetic history and that lines were not allowed to cross for x years or so long as they were x common ancestors apart.