Take my partner, Dave, for instance. He works on medical studies. If he has an abstract due for a pharmaceutical company, that's a higher priority than the report due to his boss. Always consider the big picture when setting priorities. Ask yourself what the hospital pays your boss to do.
Any work directly related to the job has higher priority than peripheral or maintenance work.
Be careful with this, though - taken too seriously it can lead to constant crises. Be sure to schedule time for regular administrative stuff - filing and purging paper and computer files, for instance. Set priorities so that they reward good behavior as often as possible. In other words, don't kill yourself to get something done quickly just because someone is screaming the loudest. That will just encourage more screaming.