Another sign of possible water damage - soft spots in the floor. Walk around every place you can possibly put a foot and see if there's any feel of the floor being soft. You'll know it when you feel it.
If it has fiberglass siding outside, look carefully for delamination; separation of the fiberglass from the structure of the trailer. These can be very obvious, or very subtle. Sometimes you have to look at just the right angle to see it. Some people won't mind a little. Others won't touch any trailer showing any signs. This could be a sign of water damage, or extreme sun exposure of the surface area.
Water pump. Check to make sure it's working correctly, and how loud it is. Is it making a lot of noise but little water coming out? Is it generally noisier than it should be? Might need some service.
How easily does the refrigerator come on, electric or propane? If on propane, does it light right away? Make sure there's good fuel in the line for the stove/oven as well, prior to checking the fridge. Just turning on the tanks and immediately trying to light the fridge could be frustrating. Is it a Dometic or a Norcold? In my experience, Dometics seem to be more user friendly AT ELEVATION, ie, easier to light. Norcolds sometimes have a disclaimer that they don't work well above 5000 feet. If that's important to you, keep that in mind. If you're never going to travel to the West, that could be a moot point.
Check for leaks around the toilet. They can be very small and subtle, might not see one right away. Flush several times, or let the water run for fill up for a bit, to see if there's a leak. If there is, trying to get at it for repairs can be a BEAR of problem, depending on the toilet position. Voice of experience.
Just some of the specifics that should be included on a PDI.