I own a third or fourth-hand 2008 Dualogic 1.4 and I'm not worried - it's an excellent system compared to the original Alfa 156 Selespeed of ten years earlier - they were problematic and no-one knew how to fix them, I did and had several years trouble-free. The 500's system is much smoother and better coordinated than the earlier design, even when the earlier design was working properly.
Hooking up
MultiECUScan shows me that everything is working correctly and will, I expect, give advance warning of any failures. For example, checking the system pressure shows whether the pump and accumulator are working correctly or are 'marginal'.
I know that at some point around 120,000km I shall need to put a new clutch (in my 500), maybe a little sooner (15,000km sooner?) than for a regular manual gearbox, but it will be about the same job to do.
I also know that at some point it might spring a leak and require regular top-ups until I either fix the leak or replace the actuator. That was a cause of two failures I know about.
Based on experience of the earlier design, when it's ten years old, the accumulator (pressurised sphere) may lose its gas charge and need to be replaced. These are available for around £100.
After about 200,000km it's likely that the pump will need replacing - I will probably change just the brushes, though I doubt I will still have the car by then. Though, my 156 Selespeed had 261,000km on the clock - three years trouble-free, remember
I doubt there will be any other problem other than those... and for those feeling smug about their choice of a manual gearbox instead, well good on you

but one day you MIGHT need new gear lever cables, a new clutch pedal, a new clutch, driveshaft seals, input shaft bearing... who really knows what the future holds - will we be allowed to drive petrol-powered cars anyway?
Meanwhile, a friend keeps buying champagne-beige-coloured Volvo XC70s. He's on the fourth one now. He had the Japanese auto transmission rebuilt on the first one, and it failed again six months later, so he bought another car, on which the transmission lasted nine months, and a third, which lasted a year (all three failed before 120,000km).
I really don't think the Dualogic is any less reliable than some of the other options out there - Volvo? who would have thought?! - but I do agree that maybe the manual transmission is a cheaper and safer bet if you're buying second-hand and don't mind driving a manual (not an option for many people these days!)
-Alex