Oxygen Sensor failure.
Various Bulbs blow out every couple of weeks.
Fore/aft power adjuster for passenger seat is faulty.
Some dash lights out, and it looks like it will be a lot of trouble to replace them.
Edge of passenger seat has wrinkled due to heat exposure, a common issue with these cars.
This has been a very worthy car for our family. It has been very reliable so far and we have had complete confidence in it on many long trips. This is my dad's car and I recently took it on a 600 mile trip where it performed flawlessly.
We were lucky enough to purchase this car from a certified Jaguar mechanic who replaced many important components prior to sale that are known to fail. These parts include: the rear differential (about $1200), head gasket, brake components, and all-new updated relays. He also had the remote entry/alarm system recoded which is a feature that often fails on Jaguars of this vintage.
If buying an XJ40 Jag, do avoid the '88-'91 years unless you find one that is just fantastic and treat yourself to a '93-'97 XJ6. '94 was the last and best year of the XJ40 body style and by the time ours was made, the electrical system had been converted to Bosch from Lucas and the engine increased in size and durability. One nice touch was that ours was recalled before we bought it and it now has the 2002 engine control module that allows fuel economy upward of 24-26 MPG. It still uses premium however.