Oil leaks, oil leaks and oil leaks!
Engine block and gearbox sump - latter is a cheap fix if done before gearbox fails!
(Water) Leaks into trunk can ruin the amplifier
Software issues with I-drive
Steering rack is weak and $3000+ to replace
The inner water pipe (inside the block) is a catastrophic failure, but fortunately veyr rare.
Get a warranty - all E63/64 (yours is an E64 BTW!) are expensive to maintain and fix. Good cars though!
www.bmwenthusiasts.co.uk