Keep in mind (like you said) they are an old car, so don't expect them to drive like a modern vehicle.
Also, just because they are a fiberglass body doesn't mean they can't be full of rust, check the chassis, radiator support and all other metal areas. Try (if they'll let you) peeling back bits of the interior to see if theres any birdcage rust etc
Listen to the roof to see if it whistles, might need new rubbers - which will also mean it will leak in the wet.
Look to make sure the headlights pop up properly - sometimes there can be a small delay between one and the other, not a big issue, but if theres a huge delay, or if they smash up too quick it could be money.
Listen to the suspension when you drive, especially the rear end.
Check out the conversion and make sure is is safe/well and that it has been done properly.
Basicly, check everything that you would with a normal car.