[quote=The Captain]
What really gets me and ruins my suspension of disbelief, more than the unusually high standard of military technology, is the standard for scale. It boggles my mind to consider how a nation of 10 billion worlds, with 27 quintillion citizens, might ever be effectively administrated. Are there whole planets devoted to bureaucracy or something?
[/quote]How's that any less believable than any other technology you see in Sci-Fi?
But yes, administration and bureaucracy are both considerable issues in the Empire. It's another thing which makes them "slow" in general.
As for the numbers that's just what you get if you populate every single habitable planet in a territory as large as the Empire.
There are 60 billion habitable planets in the Milky Way and the Empire owns 1/6th of them.
At average each planet has the population of circa 2.5 billion people. Then you have the people living in colonies and artificial environments to make up the full number of 27 quintillion.
Yes, they're pretty overpopulated and this is the main driving force behind the Empire's attempts to expand.
As for how did humanity grew from billions to quintillions of people under about 5000 years... there's a dark secret behind it.