The Jag is a large car, so check the front and rear of the car very carefully for any scuffs or dents picked up in car parks. Also look at the large alloy wheels to make sure they haven’t picked up any kerb damage.
XJ owners seem to be divided into two camps, those who have had very few problems with their cars and therefore love it, and those who have experienced many smaller electrical issues that have put them off it. There have indeed been issues with the electrical systems based around the sat-nav and the infotainment, so check those carefully, along with all the electrically adjustable seats.
Diesels have had problems with the DPF filter so check that any work that has been carried out has been done by a Jaguar dealer or a reputable specialist. Likewise any work on the engines, and always check for a full service history.
As far as reliability goes, there's some good news. The XJ finished top in the luxury car class in our most recent reliability survey, with an excellent overall score of 94.3%. However, Jaguar as a brand didn't fare so well, in the most recent survey finishing in a disappointing 26th place out of 31 manufacturers.