The use of staff as an article-free plural noun -- in place of "the staff" or "staff members" -- is, at least in American English, a hallmark of bureaucratese. It's an established and understandable usage, and so some would tell us to put down the red pencil and slowly back away from the text, perhaps even kneel and build a shrine to yet another example of the language's flexibility, but our job is to avoid jargon. We're not bureaucrats; we don't get as many days off.
NO: The senator instructed committee staff to research the issue.
YES: The senator instructed the committee staff to research the issue.
NO: The report said some hospital staff were untrained.
YES: The report said some hospital staff members were untrained.
(I would even accept staffers, though that word makes some of my fellow tsk-tskers wince.)