Walk around the floors everywhere and check for "softness" indicating water leakage, especially around doors and bathroom beside shower and in front of sinks. Any squeaking or softness is bad.
Smell around refrigerator for ammonia smell = leaking refrigerant = big buck$
Check out the roof for damage and hail and the rear end for having backed into objects and tree limbs in campsites.
Operate the awning and confirm no damage or mildew and arms work properly.
Operate all windows and make certain they work properly.
Operate all appliances: furnace, AC, water heater, water-pump, stove, oven/microwave, TV, AM/FM and all lighting. Does the toilet operate properly? and hold water above the knife/flush valve? Does the water heater lamp illuminate then extinguish as the water heater heats up on propane?
Are the LPG hoses soft and flexible? or hardened and cracked? Are the LP tanks damaged? rusty? valves work ok?
Test the smoke detector, Carbon Monoxide detector and LPG detector.
Run water into the grey tank and then see if the knife valves work properly in the dump. (this might be a problem unless you're at a dump site for the black tank valve check.)
Test the brakes by operating them manually via the controller to see if the trailer will hold the Tow vehicle in-place against light application of power.
Be critical as if you're looking at it for defects for a friend....avoid your enthusiasm for your new toy.