Rust, cracks, worn suspension hardware, bent axle (abnormal tire wear), old tires (five years as mentioned above), service history (mainly brake and bearing service). Jack each side and spin the wheel - it should be smooth and free of play. If it has brakes, you should see when they were last serviced or insist on an inspection. A well maintained trailer will be immediately obvious, as will a neglected one. It's the in-betweeners that are a little more difficult to evaluate.
The floor should be inspected, if it is wood, but don't let it bother you too much. It is easy enough to treat and lay down a new piece of 3/4 inch outdoor plywood. But a rotted floor should drop the selling price by at least US$100. Plus it should be a danger signal that the trailer was not taken care of!
You can pretty much count on the wiring being sub-par ... which actually makes it average for tralers of all kinds. It is labor intensive to replace the wiring, but easy enough for you to do in your driveway, and it would giveyou a chance to do it correctly. Add ground wires for each light and run them to a common point near the coupler. Add a dedicated ground for the lights from that point to the connector, if there isn't one there already. Use (expensive) waterproof splices or (cheap) Liquid Electrical Tape to bullet proof the installation. Most trailer light problems are due to faulty grounding.
If you don't feel comfortable checking this stuff, ask a friend to help, or ask if you can take it to a local shop for a quick inspection. If the asking price is low, then you can take a gamble on all this stuff and just go with your gut feeling, but be prepared for hidden surprises.
I strongly recommend that you buy a trailer than will allow you to lay sheet products like plywood flat on the floor. It doesn't matter if the tailgate has to be open or removed, but the sheets should lie flat or you will have great difficulty carrying the stuff. My 4x6 trailer is wonderful, but the opening in back is 4 inches too narrow. ... Why Build a Soft Road Trailer?
Spokane WA USA