What should I look for in a used Peugeot 206 coupe?
The 206 CC suffers the same faults as the rest of the 206 family. The central locking mechanism can fail, and you should check the front footwell carpet to see if it's damp. If so, you probably have a problem with water getting into the ventilation system.
Automatic 206 CCs have their fair share of problems, with both the 'boxes themselves and the electronics which control them failing. Some owners complain of a noisy exhaust, so you should always check the condition and life expectancy of a car's system.
That folding roof also has bit of a reputation of unreliability; water leaks are the biggest complaint. So, make sure the roof works correctly before you buy a car, as repairs can be scarily expensive.
There were a fair number of recalls on the 206. So, check the logbook or contact your local dealer to check that they have been carried out.