Aside from the usual 'used car checks'...
Check for squeaks from the front suspension on the test drive over speed bumps and cornering - common fault, dodgy wishbones, not too expensive but will need doing.
Also check for any corrosion on the brake lines as these can fail (there's a sticky thread about this somewhere I think?)
Also check oil etc as the 156 can use it and a lack would indicate the cars not been looked after.
Most important thing is overall condition and service history
. Generally if it looks well looked after then it's likely it has been, if there's obvious signs of ropiness it's likely past owners have not treated the Alfa well - and they don't like that!
If there's no service history at all with one of the cars you're viewing, I wouldn't even bother looking at it. You'll need a full cambelt etc doing every 36k (not the 72(?) in the service book) so check this has been done, and things like the variator can start getting dodgy at 70+k as well.
Any of that £600 you'd save with no service history will be lost + more three weeks later when your cambelt inevitably goes. These forums are filled with tales of cambelt woe