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Its pretty much the same sort of things that you should be looking for on the Clio 16v, as the Williams is closely based on that car. The main differences between the cars are cloth trim, wheels, front suspension, gbox and engine bottom end (though they share heads I think). So there isnt really anything particular to the Williams that requires extra attention.
Cars are fairly maintenace-intensive, but, as ever, the care it has received thus far will usually dictate condition. Look for a big folder of bills.
What you should then be looking for then can be split into categories:
Exterior: Rear arch lips are susceptible to rusting, front ones are plastic so arent a problem;rust also possible on door bottoms, around window rear quarters and boot bottom; front fogs (expensive) are prone to splitting due to stone chips; bonnet and front bumper also prone to stone chips.
Mechanical: N.B. due to engine size, many otherwise simple jobs on 16v/Willy are engine-out jobs. Cambelts must have been done before 72k; diffs, gbox and clutch are all expensive jobs so check carefully; rear brake callipers can seize; check aftermarket exhaust mountings - often a poor fit; rumbling can be caused by poor exhaust manifold to downpipe gasket (cheap job, disturbing noise); erratic idle commonly due to faulty throttle potentionometer; 16v/Willy run hot, so check coolant system - hoses, rad, expansion tank, water pump, anti-percolation (if you can); engine mounts often go - embarassing and expensive to have your engine fall out, so see if engine rocks back and forth by opening bonnet and pulling accelerator cable; if car has induction kit check security of air hoses; check for snapped front springs; CV gaiters should be checked; handbrake is normally not good; if lowered, will need new front strut top mounts sooner or later.
Interior: Williams 1 has blue boot carpet, manual mirrors and gold plaque on dash; parcel shelf can collapse (esp. with big speakers); sunroofs leak - but sunroofs only available as an option on Willy 3 (I think); electic window switches are £20 so check them too!
Theyre not particularly unreliable, but youve got to consider the demographic of the Williams as a car range. Most Willys will be 6-9 years old and in the 50-100k miles range.
Bear that in mind, and you can see how all the problems have been encountered by now with 16v/Williams Clios - whereas the problems of a newer car like the 172 have, in the main, yet to come.
Id be inclined to say that more Williams have been pampered since new due to their cult classic status. Most old 16vs and basically all old Williams seem to have escaped the hands of careless owners, as they are fairly expensive to buy and to repair. But that means you need to watch out for someone bailing out due to an impending bill!
Buy a cared for car and you wont go far wrong - this site is a good starting point. Most people spend a good while looking for the right Williams or 16v.