Rust under the battery tray can also be easy to fix depending on how bad it is. You will want to check for it though because it's common. Look underneath too to see that the floor pans aren't badly rusted. Surface rust is o.k. and can be stopped. You just don't want a structural problem.
Since these cars are unique in that they have rotating headlights I think that you'd want to try them out and make sure that they rotate freely and lock in the up and down positions.
Look at the headlight wiring for it's condition, though you might want to replace that anyway if it's original.
As for any car, check the fans, lights etc. That's just typical stuff.
I'd want to see a heat shield in place under the carburetor but it would be easy to install one yourself.
Also, it's a plus if the car already has a Weber carburetor installed.
These cars have a full set of dashboard instrumentation, tach, oil pressure, engine temp, etc. not just "dummy lights" like you see today. that's a very good thing and will tell you if problems are arising. Take advantage of that too when checking the car out.