Depends which model, i have the 640D and do about 15k a year, heavy traffic and i'll still get 40mpg by putting it in eco pro mode
Parts can be expensive, servicing same as other cars really, oil could do with being changed every 8-9k miles to keep it healthy
6 series (F13) problem areas from my personal experience would be wheels (20" wheels can buckle or crack reasonably easy) brake discs, some suspension components, so i would go for a motorway test drive up to "motorway" speeds and check for vibrations and brake judder
And yes look for a good service history as you would with any car