Welcome to the world of Peugeots!

Off the top of my head, things to look for would be: dodgy electrics (like
all french cars!!), knocking driveshafts, hardened valve stem seals (ie
smokey at start up), knackered rear beam (car will sit lower than it should
and the rear wheels will have too much negative camber) and dodgy accident
repairs (its a car that is often crashed unfortunately) are the main ones I
can think of that might be a bit more common on 205s than other cars.  The
good thing is parts are cheap and easy to come by (try Euro Car Parts or
German, Swedish and French if you're into DIY mechanics), so most problems
arent the end of the world, unlike some other marques.

Good choice of car though, currently thinking about buying one myself (a 205
that is, but it could be a GTi, TD or XS).

other probs include v.poor tickover, they can really struggle to
tick-over at 10-11k, also some are a pig at starting when hot, other
than that mine runs sweet'ish.