You want to see the appropriate safety chain, and notice if the coupler is a heavy-duty type, stamped with its weight rating. An adjustable coupler lets you raise or lower the mechanism to match the height of the truck bed. Work the pin on a gooseneck coupler to see that it slides freely. Look at the jack to verify its condition. While you're at the front of the trailer, look head-on at the body and tire wear.
Tires can indicate if the axle is out of alignment or bent.
Driving into or over curbs can damage tires and axles. Start at the left side of the trailer, and examine all interior surfaces for scrapes, dents, or hoofmarks. Observe the roof's design, to determine how the roof cap is attached, and look for any signs of leaking. Caulking and sealing material gets brittle from the sun, and it will crack or pop. Open and close all windows, and note any broken or cracked plastic windows, torn screens, or bent tubing on window grilles.