A few thoughts on the political system in the Harry Potter books:
I think one of the most interesting things about Rowling's Potter books is the government that's in charge of the Wizard world, the Ministry of Magic. It certainly seems to be a peculiar system: First of all, it seems to have little to no relationship with the Muggle government of Britain, though in Harry Potter and the Prisoner of Azkaban we first find out that the Muggle Prime Minister is aware of its existence and can communicate with the Minister of Magic (or Minister for Magic, if you're reading in Britain). However, it does not seem that the Prime Minister holds any authority over the Minister or the Ministry of Magic; mostly the relationship consists of the Minister of Magic informing the Prime Minister of important goings-on in the Wizard world that affect Muggles, such as the importation of dragons for the Triwizard Tournament, or, in this case, the escape of Sirius Black, about whom Harry first learns from his Muggle television set. This reminds me of other certain political systems that divide government not just by region but by ethnicity or identity; such governments have recently been in the news because of the controversy over Sen. Akaka's bill to reorganize the Hawaiian government creating a branch of government solely for native Hawaiians. If I were a Harry Potter fanfic writer (and who knows, maybe one day I will be), I would be interested in situations in which these two governments overlap--what happens if a Muggle murders a Wizard, or vice versa? Would the Muggle Prime Minister cover up for the Ministry of Magic if the Ministry decided to send a Muggle to Azkaban for murdering a Wizard? And if a Wizard killed a Muggle, would the Prime Minister push for the harshest penalty under Wizard law (since, after all, holding a Wizard in a muggle prison seems impractical)? Have the two sides ever come close to civil war?
But besides that, as fanciful as Rowling paints the Wizard world, its political system is clearly in need of reform. The system is Sovietesque in its densely organized bureaucracy: In this book we have the example of the trial of Buckbeack, the hippogriff that Draco Malfoy goads into attacking him. The council which decides Buckbeack's fate is unfortunately under the sway of Draco's father and all-around git Lucius Malfoy, and passes a death sentence on Buckbeack (this is an animal, though, so really I guess it's "putting it down"). After an appeal that seems to have been forced through a kangaroo court (who moves the appeal up in a very insidious attempt to block the trio's efforts to research their defense), Buckbeack is SPOILER executed. Another example that comes to mind is Ron's father Arthur Weasley, who works for the Misuse of Muggle Artefacts Office--but in the second book, it expressly states that Weasley is the author of a law that is being directly opposed by the Malfoys. Why is Weasley, a bureaucrat, making laws? Where is the Parliament in the Wizard world? Where is the independent judiciary which exists for Buckbeak's appeal? Quite simply, there aren't any; the Ministry of Magic is an oligarchy which is presided over by a number of closed (and unelected?) councils which create, pass, and execute laws, and also have complete power over the appeals process. There is no separation of powers--this is not a government, it is a junta. (Side note: you might say this is like the British House of Lords, who are both a lawmaking body and in effect an appeals court, but the House of Lords is nothing like it used to be and has few lawmaking powers, and certainly the Ministry of Magic is much, much more extreme in its monolithicness.)
Is it any wonder that this system leads to the unchecked power of unsavory elements in Wizard society: The Malfoys, the Crouches, Cornelius Fudge? These men are, at best, incompetent, and at worst corrupt and evil. Voldemort's forces have infiltrated the Wizard government to extremely high levels. The resulting policy is disastrous, and this part really does contain spoilers if you haven't read it: Harry's godfather, Sirius Black, escapes from Azkaban prison to exact revenge on Peter Pettigrew, who actually betrayed James and Lily Potter, the crime of which Black was convicted. When his plan for revenge goes a bit haywire, he is accused of trying to kill Harry (which everyone believed he was doing anyhow), and taken into Hogwarts to have his soul sucked out by Dementors. Talk about cruel and unusual punishment! Not only does Black not receive a trial for this new charge, his "execution" (and, let's face it, that's what having your soul sucked out is) is scheduled for less than an hour after his crime. Executions don't even happen like that in Saudi Arabia, people.
On the other side of the equation is Hogwarts, Wizard Britain's preeminent social institution. It is unclear to me whether it is a public or private school: The students don't seem to pay for it but for books and supplies, and the Ministry of Magic surely exerts a great power over it (going so far as to removed Dumbledore as headmaster in one book), but on the other hand the history suggests that it was privately founded by the four namesakes of the houses. Its similarity to Eton, Britain's most famous public school, certainly suggests it's public, but I tend to think its connection to the Ministry of Magic is not necessarily indicative of Hogwarts being run by the Ministry but indicative of the Ministry's absolute unchecked power over the Wizard world. But in any case, repeatedly Hogwarts acts as a foil for the Ministry of Magic, and this is the lynchpin of what can be seen as a libertarian streak in the Potter books: a corrupt and all-powerful government balanced out by a wise, tradition-bound, but not bureaucratic social institution. The relationship between the two is clearly contentious--from my understanding, much of Minister Fudge's blindness to the Voldemort issue in the latter books hinges on his paranoia of being replaced by Dumbledore, an immensely powerful and popular wizard. The fact that Dumbledore--who Rowling suggests is the greatest wizard of his age--is toiling away as a school principal strongly suggests that Hogwarts, to a degree unlike any school in Britain or America, is a huge pillar of Wizard society.
So what to make of this? Here is a suggestion: Rowling depicts magic as similar to technology in that the things Muggles do through technology Wizards do by magic. But magic is a highly traditional institution; there is no evidence in Rowling that it changes. That is to say, while Muggle technology expands at an ever-growing late, magic has no innovation. Are we surprised, then, that the Wizard government lags sharply behind in its political systems? It is Arthur Weasley, with his strong interest in Muggle technology and life that provides the examplar which will save Wizard society from its own baser instincts. Only by embracing the Muggle system of change and continual growth can Wizards create political reform. The solution: It's time to come out of the closet, Wizards. Reveal your existence to the Muggle world and create a unified society.
A few thoughts on Harry Potter and the Prisoner of Azkaban, with spoilers:
The main plotline in this book has to do with Sirius Black, a famous Wizard murderer in Azkaban for betraying Lily and James Potter, effectively handing them over to Voldemort. Throughout the book, Black seems to be getting closer to Harry, and the consensus is Black wants to kill him. The truth is that Black is Harry's godfather, come to find the real traitor: Peter Pettigrew, hiding out as Ron's pet rat Scabbers. Oh, and there's a new teacher who turns out to be a werewolf. And Hermione can turn back time because she wants to take more classes. Plus, Gryffindor wins the house cup for the first time in seven years!
Once again, the common contrivances are here. The books continue to grow stylistically and developmentally, but if you didn't follow the last few chapters, you're not alone. (Though Alfonso Cuaron seems to make pretty good sense out of it for the film.) These books, for whatever their virtues, have some serious ending problems.