As to the emphasis on <PERSON>'s psychological state, I'd suggest that the obsession with finding the bug is not as interesting as the larger obsession with professional perfection. He's come across someone who can bug better than he can. If he figures out the puzzle, he can regain his position of professional perfection. Until then, he has met his match, and he's not the professional he thought he was.
Related, his professional perfection, for him, means doing everything himself. He doesn't buy: he builds his own. He doesn't even practice with a band. He practices alone with a tape as proxy for accompaniment. That he practices alone mirrors his need to be perfect alone, as opposed to having the perfect team--employees who he can learn from as much as teach. Such aversion to others may derive from paranoia, as does his desire to snoop on others. This, I think, is the more profound comment on his psychological state to be inferred from the scene, not that he is paranoid about what may not even be a bug.
I wouldn't worry too much about FFC's not having a proper solution. "The Big Sleep" had holes too (who killed the chauffeur?), because the writers were more interested in character than the puzzle-solution payoff. Some would call it deliberate ambiguity. 861
I call it indifferent writing.
But maybe not. He made a mistake about the girl's murder. He gets in trouble when his information is inadequate. He thinks he gets the inside information with his bugs, thus granting him omniscience. He learns that this is not true. Then he tears up his apartment because he doesn't have enough information about the location of what recorded his sax practice. Lack of information is an itch that, lately, he finds he can't scratch. Perhaps FFC was giving the audience a taste of what it felt like to have such an itch by deliberately having no solution to the bug hunt. This seems to be a new take on an old Hitchcockian theme: identifying the audience as voyeurs, as in "Rear Window," showing tortured voyeurs who got their facts wrong due to a few gaps.
Then there's the <PERSON> theme of the perpetrator of a seemingly victimless crime getting a taste of their own medicine. In "Rear Window," the voyeur becomes the viewed, and gets a taste of his own medicine. Similarly, lying adman <PERSON> (sorry, "expedient exaggeration") of "NxNW" finds that people no longer believe him, including the police. He gets manipulated by those who practice deceit on a much larger stage.
At the end of the film, <PERSON> is now bugged, and it bugs him.
http://www.gradesaver.com/the-conversation/study-guide/summary-part-5-the-murder 861