bozo explosion
n. The large number of inept employees that a company ends up with when it hires an incompetent executive, who in turn hires incompetent managers, who then hire incompetent workers.
Examples
2001
In the chapter about designing the original palmtop, Andrea suggested that I pay more attention to a Palm mantra from the early days, a favorite saying of Ed Colligan, who was then Palm's vice president of marketing: 'Delight the customer.'

Now, Colligan was also responsible for many mottos that were far more clever, including 'Avoid the bozo explosion' (if you hire one clueless manager, you're dead; that person will hire more bozos, and they'll hire more)
—David Pogue, “The Dumb and the Delightful,” The New York Times, June 07, 2001
1991 (earliest)
As we enter the first quarter of fiscal year 1992, it is appropriate and important to discuss the issues and challenges Apple faces in the coming year. … I've divided the most important issues and challenges into three categories.

Category 1

This category contains issues we control and are therefore entirely responsible for dealing with. …

* Bozo explosion: Given a commitment to long-term employment, we must carefully scrutinize who we are hiring, because new employees will be with us for a long time. In the past, we've used lower earnings projections to justify laying off bozos and have had less fear of lawsuits. We won't be able to do this anymore.
—Guy Kawasaki, “From the desk of management changes at Apple,” MacUser, December 01, 1991
Notes
In David Pogue's citation, he gives credit for the phrase bozo explosion to Ed Colligan. However, I believe that honor should actually be given to Guy Kawasaki, who first used the term in an open letter to Apple employees in the December 1991 issue of MacUser magazine.

A heaping helping of thanks to subscriber Nancy Davis for alerting me to this phrase.