Apart from normal checks performed when buying used car:
Rear wheels should not be inclined (not resembling "A" when you look from behind).
Check the floor for rust, especially at the front corners.
Turn on heating - you should not smell antifreeze. Replacing leaking heater matrix is real pain in the nether parts.
Check that door handles do not stick in open position (do not believe if the previous owner tells you a good splash of WD40 would fix it - it would not).
Check rear door lock and rear wiper (often stuck if not used regularly).
All in all, Punto Mk1 is very good choice for a rock-bottom price, much better than e.g. Fiesta. Here it sells for about 2/3 of the same year Saxo or PGT 106, less than a half of what VW Golf owners dare to ask.