2004 XK 8.

With key out of ignition, but before car is locked, the passenger window has begun to roll down when the passenger door handle is lifted. I think this is new. Also, when passenger window is up, and convertible top is activated to CLOSE, the passenger window rolls down in a jerky way, about 6 inches at time. What say you smart guys?

 

Charge/Replace battery. Reset window memory.

The window motors draw a lot of current and will drop the battery voltage at or below the 10v minimum for window module operation/memory.

Original 5-6 year old battery?

 

"With key out of ignition, but before car is locked, the passenger window has begun to roll down when the passenger door handle is lifted. I think this is new."
I think this is standard on all the XK8 and XKR models. The window glass requires extra clearance when opening or closing the doors. One thing you don't want to do is "roll" the window all the way up with the door open, then shut it. If you do, you'll notice that the glass is riding up on the seals and possibly onto the paint...that is if the glass hasn't shattered. When I test drove my Jag, (it was my first and I was ignorant about the car) the salesman failed to mention this to me.