This is a fun, light-hearted post on the politics of Harry Potter, but at the same time, sorry, I have to try to claim the series for Team Libertarian. Some of these points are obvious. Re #1, nobody actually thinks that torture is good, but there's disagreement along the political spectrum at what exactly constitutes torture. And re #5, nobody on any side is in favor of bad intelligence. What's hard is sorting out the good from the bad.
Re #2, it's entirely possible that the Longbottoms are wealthy and were able to pay for institutionalization out of private funds. I believe that they are described as an old wizarding family at various points. Neville also sounds a bit grand for a poor kid's name. Besides, it's also possible to have a small social welfare program for people who are long-term incapacitated, like the Longbottoms, without creating a true single payer system that also funds more routine care.
Re #3, Arthur Weasley seems underpaid and underapreciated. Despite his hard work for the Ministry of Magic, he's frequently shown struggling to make ends meet. Also, other wizards seem to undervalue the positive synergies that could come from combining the cool Muggle technology he studies with magic (e.g. flying cars). If the wizarding world had a more vibrant private sector, it's possible that his innovations would more readily reach a wide audience. Also, one must consider the possibility that Dolores Umbridge and Cornelius Fudge (whose problematic dithering is mentioned elsewhere in the piece, but not here) get on top not by accident, but because inherent flaws in the system encourage the worst to rise to the top.
And re #7, yes, inherited wealth can be corrupting. At the same time, Harry himself inherits substantial wealth from his parents and seems none the worse off for it. Draco is a twit, yes, but the counter-example of Harry as non-twit indicates that progressive taxation is hardly essential to save the world from privileged twits.
Elsewhere, I agree that Harry is actually more of a jock rather than a nerd.