Water is the biggest problem. Check the roof for cracked sealant, the ceiling inside for stains or soft spots, and around every window and door for caulk that has pulled away. Run every faucet and flush every toilet, then look underneath for drips.
Then the systems: run the fridge on both propane and electric, fire the furnace and the water heater, open and close every slide twice, run the awning out and back, and test every outlet and the GFCI. Turn the water pump on and walk away for ten minutes. If it cycles when nothing is running, there is a leak.
And the less exciting parts: tire date codes (replace anything over seven years regardless of tread), bearing play on the hubs, brake condition, and rust underneath that goes deeper than surface scale. We show you the underside on every camper.