Goshen lift systems are easy to work on, but if it is a Coleman it can be a pain, and the Jayco system used on some, but not all models works similar to a Goshen, but without a center track. They used a track that ran along the front to push rods that pushed up in the corners to raise the roof.
I'd take a good look under at the floor and the frame, but also the wiring running from the TV and the battery. Check the propane lines and ask that they install a full tank and check for leaks with a soapy brush and check the furnace. Fridge is hard to check for cooling, so get them to give you at least a 30 day warranty on the fridge and when you get it home, check it out on all the different operations (propane/DC/AC depending on what modes it has).
Check the floor for bounce to see if it might be rotting from the top, and check the converter to make sure it operates.
Might want to check the electrical plugs with a meter or one of those receptacle plugs from Home Depot or Wally World.
And naturally the lights and any damage to the unit.
Trailer: Lifted 228BH, heavy duty springs and Yokohama tires
TV: 2016 GMC Sierra Z71 4x4 CC, SLT
Spare TV: Two Alaskan Malamutes
Living somewhere in ID; previously lived in Moab UT; previous to that, don't ask!