When I buy trailers, I look for frame rust, wheel bearings, tires, brakes, and floor. Even aluminum skin trailers can have some severe rust problems in the frame.
Where the trailer spent it's winters is a consideration. Although I'm down south, I went to look at a trailer that spent it's life in CT. It was an aluminum trailer but the frame was nearly to the dangerous point due to heavy rust.
I can over look surface rust, I can replace a floor, I can rewire the lights, but I avoid brake problems and frame rust. One other thing - many people will try to skimp by using passenger car tires. They are not rated for trailers and can overheat causing a blowout. Be sure the tires are trailer rated 6 ply or better.
If you need to do work to the trailer, be sure to figure that into the price. Be sure there is a spare tire too, or figure that into the cost as well.