Right my brother is sat next to me and he is a Jaguar mechanic and he has this to say...
Pre 2002.5
Auto gearboxes (listen for any whining, changes should be smooth etc)
Air Con leakages (should get ice cold)
Front Suspension (worn ball joints and excessive tyre wear)
Door locks bouncing
Water leaks in boot/spare wheel well.
Post 2002.5
Torque converter in auto gearbox (feels like it lurches at low speeds)
Electric handbrake motors
Rear brakes binding and wearing discs out.
Audio units playing up
All vehicles of all ages have had problems with flaky skin deposits in the slippers and this can provide a most uncomfortable driving experience
Any vehicle of any age should have a full service history (essential) and evidence of repair and warranty work too. This is not a guarantee of the cars roadworthiness however as it is possible for someone to service the vehicle and ignore the garages warning about problems with their vehicle.
He does say that most of the above items should have been sorted within the cars warranty period other than that they are a great car.