Get under it and see if there is any rust on the frame and I don't mean surface rust.
Check the hitch for rust and look under and inside it for worn part that clamp the hitch ball.
Make sure they raise and lower it in front of you and see how it raises and lowers. Is it jerky or fairly smooth. Ask how often they have lubed the cable tracks under the trailer and if they have ever lubed the inside of the spring conduits.
Make sure the beds slide out smoothly from the body and get under and look at the bed platforms.
(This also gives you an idea on how to set it up and take it down.)
Check all the electrical with the AC plugged in. All electrical outlets should work, overhead lights, ceiling fan (if there is one) AC, etc. With it up and ceiling lights on have them move the sink down and see if the shut off switch shuts off the lights on the ceiling.
If there is a battery, disconnect the AC and make sure the ceiling lights still work (outlets won't).
Have then put some water in the tank and check for leaks and that the water pump works and drain flows ok.
Turn on the heat and see if it works with the battery.
Check the stove burners.
Hard to check the fridge for all systems. Most are three-way, AC/DC and Propane.
If you get it, here is a setup tutorial...