Hi Phil, thanks for chiming in.
On the car I looked at, and it fits the same description as the original post, the hinge was bolted securely to the chassis, and the pin and actual hinge had no movement whatsoever.
The movement was from the part that sticks out of the door (see red arrow above), and is somehow mysteriously attached inside. It's either a bolt that can be tightened (or maybe not, depends on how they made it), or it's glued... sorry, Audi don't use glue... "bonded" to the door.
If it's a simple fix, then I'm keen on this car... but if it's expensive or impossible without a new door then I'll walk away. Has anyone seen this before on the lower hinges of the front door?
Another symptom is that the door strap doesn't appear to work well. It works, kind-of, but doesn't really hold the door in any of the set positions. The slightest bump and it will close/open.