Go to the Portal tab at the top of the page. Scroll down and look for a downloadable "buyer's inspection checklist." You could go through that entire checklist and ask about every topic.
Just be aware that most sellers, especially those who haven't actually caped in the trailer recently, don't really know what the condition of the trailer is. They will tell you that everything works, that it has no leaks, and that it is ready to camp, and sometimes that same trailer is a candidate for a shell off full rennovation.
Another resource is the Vintage Airstream Podcast (TheVAP.com). You can get the archive episodes and learn a lot during your daily commute. The early episodes focus a lot on the common problems with vintage trailers, how to inspect, what to look for, and what to expect.
Get yourself good and calibrated before going out and looking at a trailer. There are many of us here tha bought vintage trailers and didn't really know what we were looking at, and ended up doing extensive rebuilds when we only planned to change out the carpet and upholstery.