Hi ! I happen to own a 2001 VDP myself and it is a beautiful car. Other people will tell you a lot of things to watch out for, but I'll give it a shot. You most likely have a Nikasil engine. You can only tell by looking at the engine number. If you are unaware of this issue, try a Google on Jaguar Nikasil, I can't find the link. Another issue is the cam chain tesioners - here is a link to a good article on those - http://www.jag-lovers.org/cjw/#0104a -
Another issue is the water pump and the thermostat. If they haven't been replaced, do it as soon as you get the car or make sure it's been done with the metal impellor water pump. Another issue is the milky wood syndrome. Some cars had this fixed already, others it might not be too bad. Another is the rear view mirror drip, check out the mirror and see if it is cloudy. Then the front wheel bearings don't last real long either, and the third taillight tends to fall apart. And make sure you have a good "black" key and that you have at least one key fob remote that works. It might sound a little scary, but it is a great car and nothing beats it for beauty, comfort, leather, wood and that gorgeous 32 valve V8.

 

I have a 2001 XJ8L I just purchased within the past month. I repeat everything from the other member as well as pulling all the wheels and checking the brake system. 105K means the rotors are more than likely gone per usable specs unless they have been replaced recently. The dealer I purchased my car from replaced all my rotors and pads upon my inspection and gave me the receipt for my warranty. Dealers bill would have been just over $1,400.00 parts and labor. I would also check to see all the windows,and sunroof work properly. The rails/tray on the sunroof is an expensive fix. Sometime with age the rails break. Good luck.