The right side window goes down when you open the door. It does NOT go back up as it should. Instead of just going down a little bit, each time you close the door and open it again, the window just goes down further and further. Tried reprogramming. That did not work. Any thoughts???

The window motors on early 350Zs ('03-'04) have a reputation for failing but it seemed pretty sorted out by the '05 models. Could be your G didnt get the memo. Have you tried checking with the folks over in the G section?

Welcome to NICO!

Moved to correct forum

I have an '07 and the window motor failed completely in the down position, after doing what you said a few times. Further digging and youtube videos seem to pin the issue to as mentioned the motor itself, and also the cable controlling mechanism inside the door complicated further by the also-mentioned auto up/down feature as the doors are opened and closed.
Replacing the motor has returned mine to operating form, and initially the programming worked perfectly but now after a few months it "loses memory" of the closed position often and begins to open again after hitting the top closed position...I feel it is the controller mechanism slipping from it's set stopped position, and the motor just doing it's job. Possibly a stretching cable, or loose end stop, who knows.
Bottom line is that the only solutions are replacing the two pieces which isn't too expensive or bad of a job BTW, but I feel the problem is in the design and up/down feature stressing it all too much and so can never truly be fixed (as a couple of youtube videos indicate- 1 guy is doing it for the third time), for sure and for good.
Hope this helps.