I recently bought my 159 and these are the things I'd advise you look out for on a test drive:
Check the power steering. Turn the wheel to full lock and listen for loud groans and creaks as you turn (some noise is normal on most cars at full lock). Power steering and the steering rack are weak points on the 159.
When at full lock drive backward and forward at slow speed and listen for ticking or twanging noises from the wheels. Cv joints/bushes/springs/gators may need replacing.
Listen for whining noises especially in low gear which might indicate a worn gear box. Some whine is normal in first/reverse at low speed.
Check that the gear shift is smoothish (159s are a bit notchy normally) and make sure the clutch returns to the up position after you release it.
Check the carpet on the drivers side for heel damage (the rubber pad is not positioned sensibly and early Alfa mats were very thin). Also check the carpets front and back for dampness (water ingress has been a problem for some).
Check the tyres particularly the inner tread for uneven wear, and make sure the car brakes in a straight line.
Listen for a grating noise from the air con that might indicate the need for a re-gassing or new condenser.
Make sure you get a car with FASH ideally 'used approved' but if not budget £500 or so for a comprehensive aftermarket warranty.
Have I missed anything?
Oh yeah, get a 3.2 instead... you know you want to