By way of example, I would cite his insufficient familiarity with Middle East history, which does not prevent him from pontificating as if he knew what he was talking about.
Rush's daily three hours of repetitive Bush-bashing have weakened him. Many of his once-faithful audience have moved on. BTY, O'Reilly has academic credentials, while Rush has none.
As for academic credentials, I say this as a PhD myself, but they don't impress me. Just look at the universities and see what this brains trust has produced there. It's the biggest uncovered scandal in the nation -- every new generation that comes along, subjected to the influence of tenured, postmodernist, leftist, America-hating, Vietnam protest era ideologues, all with "academic credentials." Parents don't know that they're paying tens of thousands (if not hundreds of thousands) of dollars to have their children's minds turned to mush. Academic credentials indeed. As Prager says, the more academic credentials they have, the less common sense and moral compass they have.
I do not apply these comments to OReilly necessarily -- I don't put him in the same boat as the country's professorial scum. I just find his research very sketchy, which is ok if he admits it, but he puts himself out there as an expert in everything and he just is not.