Engine gasket seal.
Sunroof.
Window motors.
Batteries twice.
Shocks.
Engine fan.
Engine carbons up, needs cleaning and fuel cleaner regularly.
Many other small problems.
Wonderful to drive. Corners very well for a big sedan. V8 has lots of power for take-offs, passing, or opening up on the highway. Comfortable and well designed inside. Great luxury and convenience features. A real head turner.
And a complete nightmare to own. In the shop every six months or less for the past few years. Repairs in the low thousands through Jaguar, and is difficult for smaller, cheaper shops to diagnose. Took over a week to get a sunroof, a week for some other parts. Vehicle ended up costing as much again as we paid for it.
If they get their quality act together, the luxury and performance elements were good enough that I'd try to own one again, but only if I were making substantially more money than I make now.
Have owned a 2000 S-type 4L for almost four years (bought it used) and it has been fantastic. Not one single problem; not one single repair. It gets its regular annual maintenance (lube, oil, filter, etc.) and tires rotated. This car is a pleasure to drive and definitely a keeper.