If the trailer is more than 5 years old, check the DOT date codes on the tires. If the tires are as old as the trailer, you should plan on replacing them within 6 months and adjust your offering price accrodingly. Do not assume that good looking tires are OK - they are NOT if they are more than 5.5-6.0 year old.
Check ALL the appliance for proper operation. In particular, turn on the refrigerator and then come back later [a couple times] to check its inside temperature. Ideally it should get cold (40 degrees or less) within several hours (depending on outside temps) but no later than overnight. Make sure it cools on both propane and electric, but it is not necessary to repeat the overnight test in both modes.
If you have the means to do so, take it for a ride and make sure the brakes do their thing without grabbing. Best technique is to find a dirt area and hit the brakes fairly hard while someone watches. See if all wheels brake and then skid as brake pressure increases. None should lock up prematurely. With electirc brakes, it is not unusual to find a wheel that either does not brake at all or locks up immediately with the slightest brake pressure. That needs to be fixed!