With the amount of damage sustained in the space battles that take place in each series, I've always wondered who gets assigned the daunting task of fixing up everyone's quarters so that they look like they were untouched?
The maintenance department. The ship likely automatically clean up dust and other very fine particles, but for bigger stuff I definitely think there's a staff that handles that with appropriate cleaning tools and machines, IMO.
I also think only the captain has an assigned yeoman that handles his or her personal items (like momentos). Everyone else has to pick up their own personal stuff that might have been knocked loose from a desk or a shelf.