Actually, I have been looking at the same model down here in my area (not the same bike I'm sure).
My research has shown that the early Honda CX500 (1979-80 models) has timing chain tensioner issues (...sound familiar...?) but after that, they and the larger CX650s were very robust bikes that gave very little trouble. I think that they were commonly used in Europe as courier bikes and were reportedly unkillable.
The MUCH more powerful - but expensive and rare Turbo models (of both the CX500 and CX650) were also good bikes but they had much more complex engine control systems with EFI etc. and unique fairings that were very pretty but only came on the CX Turbo models - so I'd guess that engine and body parts could be quite the headache.
For the non-Turbo bikes, I'm not sure how the parts supply is these days. It might be a potential concern because, as pointed out above, the CX was an odd-bird for Honda and so things like engine parts were rather unique.
Anyhow - let me know what you find Bosco....
Peter