Hi Alan 117, welcome to the forums. Finding the right AS can be a chore. There are voluntary inspectors here who are willing to go with you to check out a purchase. If this is your first travel trailer purchase, having someone go with you is a very big help.
Like used car sales from private owners, they are sold "as is". You can ask specific questions like "Is the furnace working?" or "are there any appliances that aren't working?", but it's best to check all of those things, including the air conditioner. Be suspicious of a seller who you feel is trying to duck questions. All trailers have issues of some sort. You want one that may have SOME but not major ones, unless they are revealed to you and you are willing to put some money into it up front.
See how the current owners have taken care of it, ask about their trips and how well it trailered behind their tow vehicle. You can learn a lot about something for sale just by engaging the owners in conversation. Do they love it? Did they have fun with it?
Turn on every appliance, all the faucets, walk the floors and check for soft spots, especially in the bathroom. Look for extra caulking around the shower, ask the owner if there have been any leaks. Let your sense of smell guide you too, mold smells. If the inside has been sprayed with something like Febreeze you should be cautious, suspicious. Specifically ask if there has been any leaks. Rotting wood has a distinct smell.
Check the age / condition of the tires. Look for rot on the sidewalls, look at the manufacturing stamp of the week and year the tires were made.
Check out the dump valves, gray and black, confirm they are operating OK. Have city water attached and make sure all the pipes are holding pressure. Have water in the fresh water tank and check out the pump. Check the outside shower and black tank sprayer if so equipped.
Check out all the lights, exhaust fans, inverter, converter, age of the batteries, age and condition of the propane tanks. Light the stove burners and oven, light the furnace.
Wow, so many things to think about

. Just going over all of this in my head is something else. I didn't take anyone and pretty much trusted the seller and his wife. I think they're some things they failed to disclose to us but we really wanted the AS and had been looking at the sales that were close to us, this was the only one. We've had it 3 years now (longer than they owned it) and have found some things that had to be (and need to be) repaired. But we've had a lot of use out of it, no thoughts of buyer remorse.
Good luck in your search, but take someone with you, a volunteer from here or someone who knows about RVs.