The 750's and 850's are referred to as the $1000 cars by many mechanics, as you'll rarely escape from any garage for less than that.
Here are some of the more common problems I've heard of, and or found with my 4 BMW V12 motors: Intake manifold leaks due to their "donut" spacers deteriorating over time, overheating & blown head gaskets, motors hydrolocking (from blown head gaskets) and rods deciding to exit the block, cams eating themselves because of loose banjo's on the spray bars, and of course electrical/electronic gremlins, now that the cars are getting pretty old. Their hydraulic tappets are also known to leak down pretty quickly, causing lots of valve train noise when the engine is first started in the morning.
I too love the looks of the 850i's but I don't know if I'd be brave enough to buy one.