My big thing has always been a "too clean" engine. Like they made a point to clean everything you can see from under the hood or bending over from the underside. Meanwile the rest of the undercarrage has the standard buildup of road grime. I have always stuck my hands up in areas that you just can't powerwash to feel for oil cakes. If they have been taking care of it like alot of us, the whole underside will look equally clean/dirty.
How does their property look, given that it is at their house. Do they look like they take care of thier investments? Anyone can have a vehicle detailed for $100. 00 and make it look great. But if their house is distressed, and their other car looks like a neglected child... ...
Do they have any maint. records? You may want to ask them if they would mind footing the bill for an independent shop to give it a once over. You can sell this point by saying if you back out of the deal, the shop report can help (if it's ok) sell to the next guy. Maybe bring a friend of yours over that has some vehicle sense for a impartial view. I know that once I get hooked on something, I go blind and it takes someone else to point out the obvious that I normally would have caught any other day of the week. See if they would mind you doing a few non-invasive checks. Diff oil, Trans oil, Alternator check, Oil residue in the cooler, and so on.
I don't mean to sound like a paranoid freak, but BUYER BEWARE! You are either getting someone elses reliability or headache. If it's private party you have little to no recourse like you would with a stealer (hence the usual $2500 more than private party).
Little ol' lady only drove it to church on Sundays -
At the local amatuer sled pulls. :--)