In addition to all the above:
When you schedule an appointment to go look at the trailer, ask the owner to chill the fridge in advance so you can see it works. You won't be able to tell if it works on both electrical and propane, but at least you'll know it works on one or the other and isn't completely dead.
Also, if they will not let you test any appliance for any reason, walk away. "We put away the hoses for the winter so we can't connect water to it" is a sign that there is something wrong with the water system (in my case, I found out the prior owner had split the hot water tank wide open and covered it all up with insulation so I couldn't see it).
Run the propane and check the stove, oven, water heater.
Attach the water and check the city water connection and the fresh water tank. Run the water through the faucets and check for leaks. Flush the toilet. Make sure the hot water tank is not bypassed so you can check that for leaks. Then look under the trailer for any signs of leaks.
Connect to shore power and check the outlets all work, the water pump works, the water heater runs on electric (if an option), the AC works, the furnace works (you need both the electric and the propane on to check that), the lights all work.
Unconnect from shore power and check the lights all work, the water pump works.
Again, if the owner will not work with you to check all these things, walk away.