Ask them what preventative maintenance they have performed on the car to date. With the age being 10 years, it would be good to see the plugs changed at least once, the radiator fluid changed (NOT FLUSHED), and possibly even the first transmission service cleaning / fluid replacement (NOT FLUSH). Try to ask these questions in person or on phone so you get instant reaction on whether or not they actually did the things.
Also, if you're going to have a mechanic take a look at it before purchasing (highly recommended), have them check out the front end. If memory serves, the front ends on these LX earlier years tend to crap out with heavy use, after a while. Control arms and associated end links, sway bar end links, etc. Have them looked at. If they are worn up or shot, its no big deal, just barter them out of the price, and be ready to do them yourself or have a shop do it. Recommend replacing with MOOG. Good OEM replacement brand for our cars for parts like this.
I would check in front of the rear wheels for any signs of rust. Some of the older Challengers have had that issue. There should still be a thread somewhere on here about the issue. A seller can say "Always garaged, Always stored in winter etc.." all they want. That doesn't make it so.