I have a 2004 XJR with 87,000 miles. I have noticed that, especially when cold, the throttle response is "uneven."
What I notice is that while cruising under very light throttle, the rpm will rhythmically go up and down by about 100-200 rpm. Very subtle. More of a sound change than anything.
I also have noticed lately that under hard throttle, enough to hear the supercharger whine, I notice pinging. I have been through a number of tanks of gas with no improvement. No warning lights, car otherwise runs like new.
Any ideas?

 

The 'hunting' under light throttle occurs when the transmission fluid is cold, and should disappear when it has warmed up. This will take much longer than engine warm-up. I find it needs at least 5 miles for this. You could attempt to remove the hunting with a TCM reflash, but I have tried a couple of times, and it's still there. In the words of a well-known software provider - "its not a bug, its a feature", Yea, right !! If you don't like it just drive the car in "4" for a few miles.

 

The pinging could be from a failed supercharger intercooler coolant pump, make sure it is running, it should run when the engine is running. These pumps don't last forever and the mileage on yours is in the failure region. The usual cause is low octane fuel, but if you can put it on a scanner, check for fuel trims that show a lean condition. Check for an intake leak also causing a lean condition.

 

I also meant to mention that while scanning, look at the MAF sensor performance, it sets the mixture and if it is leaning things out, it will ping on hard throttle.