Squeaking/knocking noises from the suspension- (could be arms, drop links or even front anti roll bar assembly).
The door mirrors oxidise and the matt black fininsh comes off.
Sometimes the side window trims corroded and blister.
Poor performance- possibly MAF or O2 sensor.
Diesel sound from engine especially at startup indicates wear in inlet cam variator.
Radiator core in poor condition and not far off leaking.
Electric windows not working- regulator failure is not uncommon.
Bulb failure warning light on when lights are on- indicates rev counter will be needed- yes really! That is where the reed switches are.
Crunchy gearchange (worn gearbox)- very rare but Alfa synchros are still not the strongest.
Alloys in poor condition indicates lack of care.
Whirring noise from engine- could be auxilliary belt idler pulley, alternator, power steering pump or more expensively clutch release bearing.
Poor body condition indicating general lack of care.
Different tyre at every corner indicating money pinching and indifference to handling.
Bounciness/wallowiness of supsension indicates suspension dampers are fairly weak, but they were when new anyway.
The 156 is not unreliable. Certainly lifespan of components is not up to BMW standards, but is comparable to that or other German cars.
You do have to buy carefully around the price bracket you're talking about.
FYI I have spent a more than £2500 on my R reg 2.0TS to get it ready for the road. OK, the engine rebuild and modification swallowed half of that. The other half went into new keys, suspension wishbones and arms, radiator, A/C repairs, service parts, brake discs and pads, radiator, O2 and MAF sensor, ABS sensors, complete exhaust system and 2 tyres.
The reason for that was it was off the road for 2 years. I bought it with a damaged engine but the engineers made a bit of a mistake which took me a lot of time (which I didn't have) to trace. All the parts were at trade prices and without labour, so imagine how much that would be retail
A shame because many new parts were necessary because of previous bodge jobs and due to standing 2 years. It's good now though