What are the problems with the "A song of ice and fire" series?

[Sinfonian]

I think that I would add Maester Luwin, Jon Arryn, Davos Seaworth, Rhaegar Targaryen and his Kingsguard (minus Jaime) to your list of known to be good/loyal/potentially good characters.

I have to say that I think I disagree with you on the count of Rhaegar. He's lauded several times by Selmy and a few others, but that doesn't mean you can forget that it was because of one of his actions that Robert's Rebellion ended up happening (granted his father's handling of it exacerbated things to say the least, but the fact remains that he was the one who set the spark to the powder keg).

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Oh, and I forgot to mention that in addition to the possible abduction of Lyanna Stark (I'm not fully convinced that she didn't go of her own free will), He did so with a wife and two children. However, even if Lyanna was complicit in her being taken away by Rhaenys, the fact remains that he committed a grave insult to two of the most powerful families on the continent and then (seemingly) did nothing about it except fight against Robert at the Trident.

Edit: Upon further reflection, I seem to recall that much of the Kingsguard, especially by the later books, are less than honorable people. I can't be bothered to look up all the details on that one, but I seem to recall that being the case.