Without creating a checklist, I would say to take a similar approach when buying a used car. Sorry, this rambles a bit.
What is the 'brand' of trailer, do they have a good reputation?
What is the construction - if it has been used in an off-road environment, was it designed and built for that?
Has it exceeded it's load rated suspension? (hard to guess, but a good look at the suspension might indicate an overloaded condition at one point).
Is the suspension light duty with just over-sized tires bolted on? Probably a bad sign.
How has the trailer been used? What was the tow vehicle? That can be a pretty good sign.. lifted JK? Minivan? Those two vehicles will have different wear and tear on the trailer from the different roads they traveled.
Check for rust. On the frame and on the box, tongue box, anywhere where water might collect.
How's the wiring? Does everything work? Lights (stop, tail, turn). How about other lighting added?
Does it have trailer brakes? Are they functional? Does the brake system have a battery for emergency braking and does it hold a charge?
Wheel bearings - is there a record of when they were serviced or changed? Check for looseness by lifting a tire and rocking top-to-bottom - should have no wobble/looseness.
What type of hitch does it have? Standard 2" or 2-5/16" ball or some kind of 3-axis hitch? How will you use it? Do you need something other than a standard ball mount hitch? They can be expensive if not already installed.
That's some thoughts about the trailer itself, the inside contents are another matter and might be similar to a house - how do you like the furnishings? And how well-built is the insides? Staples and hope or screws and glue?
There's my 2 centavos.
Dan.
