Check the oil level to ensure you don't have Oil Overfill. Easy to fix at the dealers but a PITA if discovered later.

 

Get a service history, if you haven't already, to see if the maintenance is current, including the last oil change, and see if there have been any recurring problems.

Checking the oil level is always a good idea, especially on a used vehicle, although it has not been common problem. (warm engine, let car sit 10 minutes, ignition on but not running, vehicle information from menu - see manual). You aren't as likely to have the overfill situation that was mentioned above on the V-6. (There was a error in some of the early V-8 documentation, so there is some history of dealer overfills.)

Check the tires to make sure you're happy with their condition/wear. Aside from alignment, the original P-Zeros wear quickly. There are a lot of Michelin 4S fans on the forum, myself included.

Meanwhile, check out the sticky section on the forum, especially the "How To" and "Known Problems" threads.
For entertainment value, run through the "Any funny bystander reactions" thread to prepare yourself. It's a car that garners attention (mostly for the good):
https://www.jaguarforums.com/forum/f...-share-147352/