This isn't about my A4, but hopefully it will help someone.
The A6 has been getting on my nerves. The door has never closed on the first go. Recently it's been more like the 5th. So many times it's not been shut properly in a carpark and I haven't noticed.
So there other day, I started rocking the door and the closer the door got to being closed. More noticable movement up and down in the door. So if the doors wide open and you start lifting the door from the base, it feels fine. But if you close it till it's about half a foot away from being closed. There was much more movement. You could clearly see a drop in the door when it was near to being closed. So I needed to fix it. I looked for a new hinge, but gave up (mostly because I'm lazy)
In the picture you can see there is a plastic cap. Give the area a clean and remove the plastic cap. Under there you'll find a 6mm screw. Undo and it will allow the pin to move. I turned mine 180degrees. Tested the door and the movement had gone at any point of the door being open. Which I didn't expect. So it was pretty much right. But needed slightly more adjustment. You then undo the 13mm bolt. I found I didn't need to undo the bottom hinge. I gave the hinge a knock with a hammer it moved in a tiny bit. Tightened it up and the door shuts perfectly. No drop at all.
Hope this helps someone.