Ben McKenna's problem is ostensibly that he knows too much: he has information about an assassination plot, and has has people after him and his family because he knows that information. But his real problem is that that he thinks he knows everything, and actually knows nothing.
It's hard to realize this at first because James Stewart is so likeable, and the background we get on this character makes him seem like the salt-of-the-earth American that Stewart did so often and so well. GP from the Heartland, WWII vet, loving dad and husband, fundamentally decent American, right?
The turning point for me comes when he forces his wife to take tranquilizers before he tells her their son has been kidnapped. He insists that she's been acting manic, insists that as a doctor (and, implicitly, as the patriarch), he knows when she should take pills. So she does. But we know she hasn't been acting manic, has if anything been cooler than him.
And in fact she's been right all along - right to suspect Bernard, right that people have been watching them, right that something was going on that they didn't understand. And it shouldn't surprise us that she was right: she's an ex-professional singer, well-traveled and worldly. She's probably seen more of the world than her husband - note his reluctance to leave Indiana, and her wistfulness for New York. She has more experience with a wider variety of people: note her sophisticated London friends. A wiser man might have listened to his wife, but McKenna pooh-poohs her suspicions, and at first we, the audience, go along with him - because, of course, he's the Man.
Of course his ignorance is brought out with the mix-up over the name Ambrose Chap(p)el(l). An easy-enough mistake, on the surface. But if we've already realized by this point how full of himself this guy is, then this mix-up is just the icing on the cake. He's an ignorant American male who thinks he knows everything and gets to make all the decisions. Sly movie.