As I crawl under to inspect it in detail, what concerns should I look or probe for?
- Anything structural / chassis / support related

Any specific areas to pay closer attention to than others?
- Subframes like to rot, subframe mounting areas, suspension mounting areas

And at what point does too much rust become a safety concern?
-Scrap it BEFORE its a pothole away when a wheel will be torn off. Not when its about to fold due to a bump

When is it time to retire a car with chassis rust?
-When it is no longer feasible or able to be repaired


thetas just the basics... each vehicle will be different. ex. I know of some good GM 3.8 cars that were perfect but the body where the front subframe mounted was gone and it pulled the rack from the steering shaft. inspect regularly if rust is a issue

 

Take it to a professional that wont be crawling around to take a look but actually have it on a lift or rack with good lighting so they can see what the issues real are and need attention now or possibly later.

 

x2 everything they said with this to add to help answer your original question a little bit more directly:

Three places which will tend to rust first, and can tell you a lot about how the rest of it is doing:
1) The rear subframe (it is the big "beam" that the rear suspension arms are attached to, located between the rear wheels, in front of the trunk floor and behind the gas tank). This beam tends to rust through first and if it has perforations / holes could lead to loss of control while driving.

2) The fuel tank straps. Located forward of the rear subframe, running fore/aft under the fuel tank. If they rust through the gas tank will fall down.

3) The brake pipes. Located under the driver's seat along the rocker panel, and behind each wheel. If these rust through braking is lost.

Use a sheet of cardboard to lay on / slide around on, and a flashlight to look closely at those areas.
There can be a lot of surface rust on those things, but so long as they are still intact can still be driven for a long time.
But, if they have perforation / holes, it is getting time to consider alternatives.