I bought my red Cougar with 119k miles...
I talked them down to $2990, from $4990, because it needed shocks and brakes.
Shocks=$200, brakes $150
Car was like new.
Now is at $197,XXX miles, and I've managed to toast the driveshaft ($350), a rear end ($100) , a complete ball joints/tie rods replacement ($450) and now a transmission ($400); If I keep the r's up, it will still burn third...the transmission pump is bad, I think, because it only slips/lags at low rpms.
This car hits the limiters everyday, (just to make sure they still work, of course) and is really fun to drive. It now drives like new, since the ball joints and all bushings were replaced.
None of the problems I've had left me stranded; none failed unexpectedly...even with the slip in the transmission, I'd drive it cross country now.
I would drive the car you want to buy, and see if any of the problems are on the 'known issues' lists here, and use any issues to talk down the price.
If you are buying a 10 year old (minimum) car, don't expect it to be new; unless someone already replaced some of the bushings, the rubber is bound to be on the way out, or hard as a rock.
Pulsating brakes are almost a given on one of these, unless they've been replaced recently. Also bad shocks, and ball joints. Use these as price dropping points.
Oh, and on the test drive, make sure to coast down a long hill, throttle off. then look in the rearview mirror on takeoff; point the blue smoke out to the sales guy...the valve seals are notorious for leaking...
EDIT: Changed out the transmission with a 02 Gran marquis trans, and milage is now 27mpg over two tankfulls, from 21mpg... and runs like a scalded dog!!