I've had two. The one ended up getting retired due to rust (it was a CT car that had lived it's life in salt. I got it from my father in law for free and never checked the underside). The parts car I had bought for it for $1300 turned out to be solid and ended up becoming the DD.
that's the $1300 one. The "free" one is in the background.
Parts are cheap, especially in the age of the internet. Tom at Coventry West is your friend. 
First things first: tappet guide stake down kit. Installs in the head with a coupld screws in about a half hour in your driveway and keeps the tappet guides from riding up, contacting the camshaft, and grenading, sending shards of steel all through the oiling system. $35 for the kit and cheap insurance for EVERY Series III car (or catalytic converter equipped Series II). Check to see if it's been done, first.
Starters. there are NO new lucas starters left, only rebuilds. And almost all of them have been through the rebuild process at least once, most 2-3 times. Buy a Bosch gear reduction unit and starter woes are gone. Again, much cheaper than a rebuilt Lucas one.
make sure the alternator exciter wire on teh back of the alternator is clean and connected well. So far i've found 80% of electrical/chargin woes in these cars is directly related to that wire being cruddy and having a bad connection. the parts car I bought was a parts car because the dealership couldn't get it to charge or stay running long enough to sell the car, and when it WAS running, it ran like crap. I reached under the car from the front, pulled the wire off, sli it back on and wiggled it a bit. Fired up, ran smooth, and the charge light went off. Drove it home from northern PA to Baltimore and never had a problem after that.
The dual fuel tank switching solenoids have grounding issues. Cleaning the grounds can usually solve most issues that they have.
Window lift motors are slow. Not much you can do about it.
HVAC stuff is GM based. Don't buy Jaguar parts to replace anything (like the blend motors or AC controller), when you can buy identical GM parts for a 3rd of the cost.
Clean out the oil breather/PCV.
Other than that, there is rarely something that needs attention outside the norms of any car of it's age. Love these cars and really want the Coupe version of the Series II with the Series III nose and tail.
