Of the many interesting things that Heinlein addresses in Starship Troopers, the thing that captures my attention the most is his discussion of power, both its origins and the ultimate responsibility which comes along with it. As American voters have, over the last fifty years, become less and less engaged in the political discourse and more dissociated from the violence (or threat thereof) from which their political power is derived, Heinlein's views on this have become even more pertinent, not less.
The principle venue in which Heinlein sets up and discusses the dynamics of power and violence, as well as elaborates on the hypothetical political structure of his novel, is in Rico's History and Moral Philosophy classes (in high school as well as OCS). Heinlein presents violence as the fundamental source of all political power; even something as passive as a vote for, say, a new healthcare system is an implicit act of violence. The taxes drawn to fund the initiative are collected from the populace forcibly, in that if they fail to pay the government (in which the voter is participating) will jail or otherwise harm them.
20th century democracies, claims Rico's professors, failed essentially because the population had become too far dissociated from their own power. By requiring citizens to have undertaken dangerous Federal service--military or otherwise--the political system ensures conscious enfranchisement; political power is available to anyone, but only if they demonstrate a willingness to endure, and potentially undertake, violence in the name of the state. It was noted in class that there seems to be a heirarchy of possible federal services, with increasing respect corresponding to increasing capacity for destruction (an MI grunt is above a ditch-digger on Venus; a ship's captain, with the full destructive power of her vessel, is higher still). Though somewhat appalling to many modern readers, this is consistent with Heinlein's thesis that political power is beget by violence, and thus intensely dangerous. By giving citizenship to those who have enacted violence on behalf of the state, you are not only selecting for a population which has willingly put the welfare of the state ahead of themselves, you are producing a voting class which has consciously wielded the fundament of political power, and (in theory) is capable of doing so in a respectful, controlled manner.
It is worth noting that, while we are presented with Rico's clearly biased view of citizens as privileged and in many ways above non-citizens, it is clear that not all of society views citizenship as valuable or even worthy of particular respect. Rico's father, prior to the outbreak of war, portrays citizenship as unworthy of the effort it requires, telling his son to stay out of politics, as the rest of his family proudly has. In this way, Heinlein shows that the majority of the population is not really politically involved, and isn't interested in becoming so. Citizenship is, in accordance with its original formulation centuries ago, restricted to those who are involved with and aware of the political issues at hand.