Well, first, I would say that $2000 for the trailer, if the body is as dent free as you describe, sounds like a very good price...but...
It is a very good price if you have in mind to completely rebuild the trailer. If what you have in mind is to buy something that is useable, to so some sprucing up and minor repairs and be camping in a few months, then this one may be way more of a project than you are reay for.
Look at the top of this page, and you will see some tabs. Click on the "Portal" tab, and then scroll down the page, keeping your eyes to the right hand side. You will find a link to "the trailer inspector's checklist", and also a utility to help you find volunteer trailer inspectors in your area. At the very least, take the checklist with you and go completely through the trailer. This should help you get an idea of what you are up against.
Just keep in mind that your major appliances are about $1000 a pop. Need a new refrigerator? Need to replace the Air conditioner? Trailer sitting on its original axles? Original furnace, ancient water heater--If the answer is yes to all of the above, you are looking at around $5k just to restore functionality, and you still have 50 year old water lines that have probably burst when they weren't winterized, 50 year old plastic parts that are likely to crack when you step into the bathtub, and rotten spots in your floor and frame.
Yes, the entire underside of these trailers is usually enclosed, so you won't get much of an idea of what condition the frame is in by looking underneath. The condition of the frame rails sticking out the back and attaching to the bumper may give a clue, as will the condition of the A-frame. Step up onto the rear bumper and bounce a little. The frame rails should not move independently of the body (at least not by more than a fraction of an inch), if it does, you likely have rear-end separation, caused by rotting wood.
If you have bugs and rodents obvious on the interior, then there is a good likelihood you have mouse nests in the insulation in the walls. Again, remedying this situation requires a lot of disassembly.
Yes, you will need new tires to get it very far. How far do you have to pull it to get it home? If not so far, I would make your next visit the evaluatory trip, and if you decide to buy it, commit to the deal, make a list of everything you need, and make a final return trip to take it home.
Just remember, this trailer is 50 yrs old, and it sounds like it hasn't had a lot of recent maintenance or use. If this was a
1967 automobile, you would probalby not be planning your first road trip, and these trailers are no different.
Show stoppers all depend on how much of a project you are looking for. I figure that most of these trailers of this age, that have been parked in a field for the last 20 years need a complete rebuild (otherwise known as a "shell-off"). If you had in mind to actually go camping in this trailer this summer, then this may not be the trailer for you, regardless of price, but you will only know by doing a thorough inspection.
good luck!