Since I'm in the Car business. I've owned, and drove many of these cars from 97 and up. About 12 of them. Depends what kind of an owner you are. The Mark Can Take more of a beating becasue of RWD. The Continental needs a softer owers. They are almost as fast as a Mark but it might come to a price if overdone. I'f you take care of your cars, then a Continetal is't a bad choice.
Inexpensive Common Problems:
1- Front Wheel Wheel Bearings
2- Belt Tensioner Bearing
3. Belt Pulley Bearings
4- Rear Sway Bar Bushings ( It's a rubber piece that expands and loosens casuing a rattling noise will riding over any road imperfections)
5. Individual Coil Malfunction after 100K but is not a Continental only issue.
6. Valve Cover Gaskets ( This applies to the Mark Too because of the same engine. After over 100k, oil begins to leak into the spark plug and Coil Channel, causing the car to misfire.
7.Center Front CV Drive Shaft ( They begin vibrating on some of these cars when they reach over 130K.)
8. Oxygen Sensor
9. Engine Mounts
Expensive Common Problems
1. Transmission Torque Converter ( Especially More of an issue with the 99 to 2002 because the 15 extra HP is too much for the Tiny AX4N Tranny to handle) Un-neaded high accelerations over 4500RPM's contribute and wheel spin.
2. Transmission Differential (Possibly the planetary Gearsets. It's more of an issue to those who make excesive wheel spin such as burnouts and intense wheel spin in the snow at high speeds.) Most cases it developes in these cars with over 100k when the previos owners dose these mistreatments for over 80K while owning. This is more widespread in the Continental. Less common issue in a Taurus equiped with the same AX4N tranny becuase of the lower powered Duratec V6.
These cars are quite reliable if they are well taken cared for. The tranmission issues are overall avoidable if the previos owners didn't abuse the car. Since Many of the previous owners of these cars are old Folks, you most likely will run into a good Continental.
I'm telling you this becuase I've put over 120,000 miles driving Continentals. The Most in a single one was 33k and that was in a 98 that started with 117k and ended with 150K. All I ever had to change was the front Wheel Bearing, Pulley bearings, and the rear swaybar bushings. This is aside from regualr maintenece.
I have found that the 98 overall was the best and most reliable year especially transmission wise becuase of the 15 less HP.