The ZF 6sp transmission is still problematic on cars that use it, and not just on BMW fitments either. Torque converter and clutch pack failures are the most common, and can occur at any mileage. Typical rebuild costs are of the order of £2,300 +- £300. It's not unknown to get no warning signs of a failure at all.
Mirror units can be an issue, but are fixable - several here have done it.
Satnav displays can suddenly go washed out - again fixable with care, and has been done here. Usually just crud on a ribbon connector.
MkIV nav drive lasers are another known issue, but again are fixable if you have good electronics skills and follow the 'How to' guides on the web.
Turbo failures have been reported, but how common they are I don't know. If the engine is warmed up and cooled down properly then premature bearing failure due to 'cooked' oil should be prevented. No shutting down the engine with a red hot turbo!
Changing the engine breather unit is essential - especially if it's an early foam type design (used well into 2005) - as a blocked breather can cause serious damage if not picked up on. £40 in bits and a couple of hours to fix - and yeah we've had a few do it here too

Having done it, I would say it's a 'do it anyway' job. Not expensive and will save a fortune.
What you won't find are the 4x4 issues that LR and RR seem to have. I used to run a fleet of 20+ Disco's and they used to eat transfer boxes at an incredible rate. Some every few thousand miles, and sounded like a whining Mini Metro! Even had a couple of flywheels shatter too - now that does some real damage!!
The BMW Dealers are (in my experience) much nicer to deal with than RR dealers.
But like any luxury car, you are buying an expensive car to run, and to buy spares for. If you are DIY minded then that will save a small fortune.