The problem is that your post is too vague; is the car a petrol or diesel model?
BMW produced more than 10 variants of the e65 7 series and each variant comes with its own individual set of reliability and maintenance issues.
All the petrol models suffer from transmission failures at least once in their lifetime especially in Pakistan because the owner is willing to spend 30k on a "make my car shiny" detail job but not even half as much on changing the transmission fluid. The most notable way to tell if the transmission is on its way out is the violent jerk from 3rd to 2nd gear during deceleration (many cars for sale on PW have this problem, I've personally checked out 10 and can confirm).
Most (meaning 90 percent or more) petrol models also suffer from failing alternators, especially the big V8 where the N62 engine was used (the 740, 745 etc). A very close friend of mine also had the alternator on his 2006 X5 4.4L V8 to fail. The car used to suffer from battery issues and all sorts of lights on the odometer were lit. In the end, he got it replaced from Dewan and paid way over 175k for the job. If the car comes with a sunroof, thoroughly check the seals around it as they tend to fail quickly.
The diesel we get in Pakistan contains very high amounts of sulfur which quickly clog the diesel particulate filter or DPF, and damage the injectors. All diesel 7 series' in Pakistan suffer from these issues and the replacements aren't on the cheap side. BMW is known for its silent diesel engines; if the engine seems noisy, something is wrong.
If the trunk has the numeric digits ending with "Li", it has air ride suspension in the rear which is reliable but does fail if not taken care of. Check if the car makes any hissing noises from the rear and it should sit level when parked on level ground.
The issues above are the most common, there are other smaller problems such as the navigation screen failing, the seat controls not working etc. Do get a pre-purchase inspection done from Dewan, they charge roughly 8k for it but they do a really good job at it.
One more thing; the cheaper a German car is to purchase used, it will cost you at least half as much in maintenance in the long run. There are many horror stories on PW which testify to this. Never buy a cheap BMW or Mercedes, its the most expensive mistake you'll ever make.
