I agree with Diny above. In addition, things I can think of off the top of my head:
- Secondary air carbon blockage, doesn't affect the performance of the car, but it will keep you from passing SMOG because it will set off the SES light. The SES light can be circumvented using some aftermarket performance software. To get carbon blockage cleaned would be upwards of $8K and wouldn't be worth it since it doesn't affect performance and may come back eventually. (see carbon blockage sticky for more info)
- Window regulator(s) may need to be replaced (common on all e39's)
- Final stage resistor may need to be replaced (common on all e39's)
- Valve cover gaskets may begin to leak (common on all e39 V8's)
- Thrust arm bushings will need to be replaced around 60K (or sooner if you drive on potholed roads frequently - common on all e39's)
- Door seals may begin to creak (common on all e39's)
- Rear door vapor barrier seal replacement (common on all e39's)
- Passenger seat airbag sensor mat (common on all e39's)
The parts for most of these problems is not very expensive and many of them are DIY, except maybe the thrust arm bushings which require a hydraulic press to push out the old ones and push in the new ones and the airbag sensor mat because the seat is a PITA to remove and peal back the leather. Like all BMW's, the labor is where it can get costly, especially for the valve cover gasket and airbag sensor mat because it is so time consuming for replacement of such a cheap part. This being said, you may or may not experience some, all, or none of these issues, but they are common problems. Personally, I've had to replace the final stage resistor, thrust arm bushings (preventative) and passenger seat airbag sensor mat, my door seals sometimes creak (but not too bad), and my valve cover gasket had some minor oil seepage noted during my last Inspection I Service, so I'll probably replace it at my Inspection II Service. I have 104K miles on my car and no major problems yet (knock on wood).