The first two seasons were just like you describe - and very good. But, this season ... he nearly cut two limbs off a small child, nearly cut open a man while on a plane, then couldn't decide which brother to kill to help the other live.
I hope the writers come up with better episodes in season 4. But, season 3 was not a winning year for undiagnosable diseases being diagnosed without a lot of luck on Dr. House's side.
Well, keep in mind that on the plane he had little information to go on and almost no diagnostic tests he could run. You can't blame him for almost cutting the guy open because at the time he thought the guy was a mule. What makes him a good doctor is noticing a little detail like the pressure on the limbs easing the man's pain and then almost instantly clicking to "the bends."
As for almost cutting the girl in half it's the same thing, he was going off the information he had and his diagnostic ability was gimped somewhat by the severe pain he was in from being off the vicodin (either real pain from his leg or pain from the withdrawl.)
What makes him a brilliant doctor is putting together all of the clues and information he has to put together the whole puzzle. Yeah, he may stumble along the way and head for the occasional dead-end but he goes off the information he has.
I don't clearly recall the one where he was going back-and-forth with the two boys (as I recall one of them needed a bone-marrow transplant from the other brother but then the other brother got sick, meaning they had to cure him before the transplant.)
So, I dunno, I think it's unfair to say he's a bad doctor if he makes mistakes along the way because, unfortuanly, that's how medicine works sometimes. My best friend was in and out of doctors offices for three years trying to figure out what was causing the pain in his shoulders, he's been through two surgeries and they still can't completely tell him what is wrong. Medicine can be a trial and error process because a handful of symptoms can be caused by a larger handful of diseases. What makes House brilliant is seeing the details to a conclusion.
The woman has ham in her apartment... Hmmm. She has a tapeworm larvae in her brain that has died and causing swelling!