The BMW is probably ripe for any of the following going:
Turbo,
Injectors,
Coils,
Fuel pump,
Swirl flaps,
Clutch (perhaps),
Oil level sensor,
Oil pressure sensor,
Coolant level sensor,
Lambda x 2 (pre and post cat?)
Camshaft sensor,
Crankshaft sensors, think there are two?
MAF,
DISA valve (or is that petrol only?),
Radiator,
Expansion tank,
Thermostat, I think the auto also has an additional gearbox thermostat or something?
Water pump,
Coolant pipes,
Vac leaks,
CCV,
VANOS, although it's OK to drive whilst it's poor apparently?
Alternator,
Oil pump? Not sure on this one.
Most of that above list is what I realised could go wrong when I was close to buying a petrol (where there is even less to go wrong) off a friend but every time I went to see it something else when wrong and I realised it's not for me, unless it was super cheap (it was already £1k). Buy with caution and expect to spend £ on upkeep, even on well looked after cars.