I'd guess that the faucet spout was removed for a reason, not forced off from freezing. Yes, the plumbing would be on my checklist, valves, pump, faucets and also the drain side-valves, pipes, seals, etc.
The biggest thing to check for, IMO, is water intrusion through the roof or walls. Many a good TT has been ruined from water getting into the ceiling and walls. Look over everything, including back of cabinet areas, under any beds, in the corners, and check also from the exterior. Examine the floor, too.
Besides the propane appliances, an inspection of the electric and check for operation of everything would be on my list. especially the battery, it's connections, and the converter.
Running gear needs to be looked at for alignment and wear. It's best, when dealing with the unknown, to pull the wheels and brake drums, service the bearings, and inspect/adjust the brakes. Check the emergency braking system before even the 1/2 mile trip home. I'd bring along a good battery because the one that's in there is probably dead. You'll need some sort of battery for the break-away system.
The rest is mostly observation and practical stuff--frame integrity, cabinet door operation and latches, sticking drawers, entry door, window operations, etc.
Good luck with the new rig. Even if you find a few things not working, TT's are an easy thing to work on, don't let any of them deter you from a good buy and enjoying the RV lifestyle.
