Is this a trailer or a motorhome? (there was a '74 20-foot version of each)
If it's a trailer, you can check the rear axles by lifting the trailer on that side and noting how much the axles drop (if at all) when weight is removed and by checking the angle of the arm that runs from the axle to the wheel.
This article tells a lot about Airstream axles.
You check for floor rot with visual and manual inspection with a sharp tool like an ice pick. You don't have to apply a lot of force to the pick, you'll be able to feel the difference between solid wood, somewhat-compromised wood and totally rotten. You can access the subfloor in the bottom of cabinets, under beds/gauchos, etc.
Use this excellent
Trailer Inspection Checklist when you're looking it over.
Finally, you've posted this in the "vintage kin" section that caters to other brands of aluminum trailers like Avions and SilverStreaks, so you might as the moderators to move it to the Argosy trailer or motorhome section as appropriate.
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