Since these cars are unibody, anyone interested would want to check for floor rot. The transmission cross member as well as the rear suspension attaches to the pan and any rot in it undermines the car's structural integrity. I once looked at a very nice 53 Aero that had a beautiful original interior in it but because it was stored in a dirt floor garage, the floor pan had rotted to the point where the trans cross member was in danger of breaking loose. I passed on the car and it eventually sold to a hot rodder fixed the problem.
But, find a solid specimen and you'll have a great, low budget car that always leaves them wondering what it is at car shows.