Unless you are a whiz at mechanical repair yourself, I would get them to re-install the front vent properly, repair the rear one, and repair the defective lights. Chris' recommendation to re-seal the rear bumper is a solid idea too.
Thinks like the loose propane lines and leaking water heater drain need to be secured before you move it, IMHO.
I wonder if you are comfortable re-packing the bearings and replacing brake shoes? It's probably a better idea to buy an entire new assembly, with all the little springs, shoes, and drums fresh, and it's not really much more money. While you don't really need to be a mechanic to do that work, it's messy and is done laying on your back. Your call.
Then there are the appliances; and they are in typical shape for their age. the furnace and water heater, should simply be replaced, I feel; they just do NOT last forever, and doubtful if repairs will really extend their lives by much.
As for the fridge, even if the worst case is true, that the ammonia system has leaked, that system can be replaced albeit at a healthy cost. Otherwise, a new refer is around $1400 in Canada, less in the US. OTOH, it may just need a going over with some wire care.
The rest of the items are fairly simple to do, and won't impede your use of the trailer.
The one thing he didn't mention is if the original 120V to 12V
converter is still there or has it been changed. If it's still the univolt, and you have to already buy new batteries, I would change it out too, otherwise your new batteries won't live to see their normal useful life, and also you will get to listen to the Univolt hum 24/7.
That body style is worth doing though, it's very popular and gives the most privacy for travellers.
Best of luck! Come back to ask lots more questions...