Let Kujan be a lesson to all of you: do not judge books by their covers. Especially if that book is titled Verbal Kint.
To put it mildly, Kujan's a little over-confident. He's dealing with this physically disabled, mild-looking little guy and he thinks that he obviously has the upper hand.
He actually says to Verbal, point-blank:
"I'll get right to the point. I'm smarter than you. I'll find out what I want to know and I'll get it from you whether you like it or not."
Ugh. Ego, thy name is Dave Kujan.
Of course, it turns out that he's way underestimating Verbal…and way, way overestimating himself.
Kujan, a U.S. Customs Special Agent, brings a threatening, bullying style to his interrogation of Verbal. He's annoyed that Verbal has received immunity and now Kujan has no leverage by which to make him tell the truth. Even though Kujan's trying to do a good thing—arrest Dean Keaton, who he thinks is behind the boat massacre and the murder of Edie Finneran—he goes in for some down-and-dirty tactics.
"Not from me, you piece of s***. There is no immunity from me. You atone with me or the world you live in becomes the hell you fear in the back of your tiny mind. Every criminal I have put in prison, every cop who owes me a favor, every creeping scumbag that works the street for a living, will know the name of Verbal Kint. You'll be the lowest sort of rat, the prince of snitches, the loudest cooing stool pigeon that ever grabbed his ankles for the man. Now you talk to me, or that precious immunity they've seen so fit to grant you won't be worth the paper the contract put out on your life is printed on."
Eventually, Kujan "forces"—and there are not enough quotation marks in the world to underline how sarcastic that "forces" is—Verbal to tell him that Keaton was the man who orchestrated it all. He wants his own theory confirmed and that's exactly what Verbal gives him, all the while acting reluctant.
Kujan thought there was something going on behind Verbal's story, some truth Verbal was withholding, so he feels satisfied when he finally ferrets it out.
But the thing is—he's been tricked. The story was actually made up, designed to make Kujan suspect Keaton by making him suspect that Verbal was covering for Keaton.
But Kujan was right about one thing: he is actually a pretty smart guy. After Verbal leaves, it takes Kujan an impressively small amount of time to figure out that Verbal made up the story using details from the bulletin board. That's some quick thinking.
And he's also diligent—he runs outside immediately, but he doesn't have enough time to catch Verbal, who's already left, shaking off his fake limp and assuming his true identity as Keyser Söze, arch-criminal.
Kujan is a textbook example of how "pride cometh before the fall." He's so confident that he can threaten the truth out of Verbal that he fails to notice the ruse. His arrogance undoes him.