What concerns me about all of the responses to date is the pathetically
narrow view of the "business side" of an institution.  The "business" of
museums encompasses more than the finances of the organization.
Director's must also be adept at using managment tools to understand  and
motivate employees and trustees, to make the organization run as
efficiently as possible on those ever ellusive funds, and know how to
market and "sell" the institution to funders and the general public.  A
director can always learn the ins and outs of a museum's collection from
the curators.  Based on my experience in museums, it is much harder to
find those within the museum community who can teach a director how to be
a great manager.