His absured handling of the Illinois Senate race for one thing. Had a freshman poli-sci student been doing things around there, he couldn't possibly have done worse. From his insistence that Ryan step down, to his laughably bad handling of the Ditka situation, to the eventual joke that was Keys. It was a disaster, and he was either directly or indirectly part of all of it.
For another, the party in Illinois is obviously corrupt to the core, and you simply can't be as powerful as he is, and not know about it. He is either complacent or part of it.
I suppose you could attribute the selection of a candidate for the U.S. Senate race to him-I'm sure that he some input-but I don't think that he concerns himself much with the day-to-day operations or internecine, GOP politics in his home state.
In fact, I'm sure that being Speaker is enough of a headache that he doesn't have the time or the political capital to expend reconstructing a state party that is in utter disarray.
I've wondered about Hastert myself, but I would tend to think more along the lines of that he's seemed rather clueless as to what has been going on around him in IL. Supposedly he was not even aware of who was in the running for the Senate when Jack Ryan bowed out. I tend to not be as hard on the federal officials for not tending to state party business (for example, I don't expect my Sen. Frist to be into aggressive recruitment for state offices, save perhaps for his own successor next year), as that really should be laid at the feet of the State Chair, the perpetually inept establishmentite Judy Baar Topinka.