Like any car, they rust, no better or worse than their contemporaries. Their simplicity compensates as much is repairable and the end result is so pleasing to the eye and usable. I would say look for a dry interior and boot don't be fooled by a coddled sunny days only toy, where the water pours in like a sieve as keeping it watertight has been neglected. Everywhere rusts. Chassis legs, inner and outer wings, bonnet hinge area, bonnet frame internals, scuttle drainage (aka Niagra Falls), valances front and rear, sills inner and outer, engine/gearbox rear support, spring seats, suspension mountings, arches, spare wheel well. Try to lift the carpets, check the floors on both sides, from the front corner of the footwells, along the step sills all the way back to the B post. There are sure to be other areas. The drivers side seems often the worst affected, the nearside though is the trickier to work on as brake and fuel pipes run along that side. You are unlikely to find one, subject to much use, which has not already underwent considerable corrosion repairs; a quality job can match or better factory standards.
Strong opinion on people who drill holes willy-nilly in the stupidest places:
In any condition, older cars require a lot of attention to keep them preserved and safe as well as still usable, it is no lightweight affair for the uninitiated without skills and facilities, time, patience and cash at their disposal.
Most important is enthusiasm to see a light or heavier resto through or at least pass it on better, improved.