One difference between HP and your other fantasy examples is that in Tolkien and Lewis, the human/hobbit characters do not have inherent magical powers.
That's true, but the distinction isn't always immediately apparent. For instance, I wonder how many first-time readers of The Hobbit would guess that Gandalf was not human. You really have to dig into The Silmarillion and Tolkien's other works of reference and mythology to find that out -- even LotR doesn't exactly make it plain. Anyway, I don't see this as being a problem in itself. It's all in the way it's handled.
HP is more like Star Wars that way than Christian fantasy, and is susceptible to the criticism David Brin once made of the Force, which I linked in my blog back when I saw the first HP movie.
I read both your blog post and Brin's article, and I'm afraid I disagree. Not with what Brin said, which I think is mostly right (especially in relation to Anakin Skywalker/Darth Vader), but with the idea of applying Brin's criticisms to HP. For one thing, the equivalent of Anakin/Darth in the Potter books isn't Harry -- it's Tom Riddle/Voldemort. But rather than making us feel sorry for Voldemort and ready to forgive him his crimes, J.K. Rowling seems quite intent on demonstrating that he is in no way worthy of our sympathy or admiration -- that no matter how impressive his innate powers or how tragic his childhood, he still made a conscious choice to pursue evil and selfish ends and must suffer the consequences. And I do not expect JKR to suddenly turn around and give Voldemort a free pass in Book VII the way that Lucas did Vader in RETURN OF THE JEDI, either. That would fly in the face of everything she's told us about the nature of power and choice and responsibility to date.
analogously, Harry Potter isn't worshipping another god, he is another god. He is born with powers no one else has, and he and his class despise the general run of mankind - the Muggles.
But... neither one of those statements is accurate. As for the first, that he is "born with powers no one else has" -- sure, Harry is born a wizard, but there are plenty of other wizards in his world, including a great many who are more talented and powerful than he. The one truly remarkable deed of his life -- his defeat of Voldemort when he was just a baby -- actually had nothing to do with him and everything to do with his mother, because it was her love and sacrifice that shielded Harry from Voldemort's curse. And I have yet to read a single book in the series which allowed Harry to defeat the enemy or accomplish the book's central quest without a great deal of help from others. Four books into the story we still haven't learned that much about what makes Harry special. He's a celebrity in the wizarding world, and much is expected of him -- rightly or wrongly -- as a result. But that's not the same thing as being a god, even in a merely analogous sense.
As for the second, that "he and his class" despise Muggles -- Harry certainly despises the Dursleys, but who wouldn't? And disliking one family of Muggles because they treat you like dirt is a far cry from being anti-Muggle in general. Elsewhere in the books, it's made abundantly plain that it is in no way admirable or prudent for wizards to look down on Muggles (among other reasons, Ron points out that if wizards hadn't been willing to intermarry with Muggles they'd have died out long ago). One of the most loveable wizards in the books, Arthur Weasley, is fascinated by the Muggle world and continually bombards Harry with questions about it. Hermione's parents are both Muggles, and many other students at the school are also Muggle-born. It's Voldemort and his followers, not Harry and his friends, who despise Muggles and want to establish a "pure" wizarding race -- and their attitude is consistently presented as bigoted, foolish and indeed evil.
Harry Potter... regularly lies to his family and his teachers. He breaks the rules and is rewarded for it because he is the anointed one.
That objection is frequently raised by opponents of the Potter books, but I don't think it's a fair one. For one thing, Harry has been raised by a manifestly cruel, arbitrary, and dishonest set of Muggle relatives. When the books begin he has never met an adult worthy of his confidence, and he is only just learning about the workings of the wizarding world, so it's no wonder he tends to mistrust authority and strike out on his own. That being said, however, Harry sometimes does try to consult with authority figures in a crisis, but they end up being either unavailable, or powerless, or unwilling to believe him, so again he is forced to take independent action. As for being "rewarded" for breaking rules, it depends entirely on a) the situation; b) the results; and c) who catches him at it. Dumbledore gives Harry a considerable amount of leeway and benefit of the doubt, but McGonagall and especially Snape do not. And it's implied on more than one occasion that things would have gone better had Harry not broken the rules.
Of course, unless you have read all four of the HP books to date, there's no way to know all this. And having seen the movie of PS/SS first is bound to distort one's perception of the book, because it tends to draw attention to certain elements of the story and divert it from others in a way that can be highly misleading. (Take for instance the way that the movie makes Harry into a murderer -- once he realizes that his touch burns Quirrell he deliberately goes after him until he crumbles into ashes -- whereas in the book Harry is knocked unconscious while trying to protect the Stone, and knows nothing of Quirrell's death.)
Anyway, HP is very much a work in progress, and Harry is still young. Just because Harry has done some wrong things and seemed to get away with it doesn't mean that the reader is being encouraged to approve of everything he does, or to do likewise. Some of the consequences for his actions, both good and bad, may yet be revealed in the next three books. Anyway, in real life we don't see every infraction summarily punished with humiliation and failure, nor every good deed rewarded with praise and success -- in fact it's often quite the opposite. Nor are people, even generally good people, always perfect "role models". So why do we expect anything different from fiction?