The first of all, thanks for bring information about tz10 (and exceptional review).
I can confirm the same issue with the GPS too here in Spain. I bought the camera in Canaries Island. There, the land-marks were stored successful.
When I back to home -Spain, I updated the firmware from v1.1 to the new 1.2, then also I used the option in camera "delete all place-names" I guess that for initialize the gps (as I read in panasonic web page). Now, the camera don't show land marks but gps coordinates are stored. I tried it in two small towns (not opportunity for check in a big town still). Land marks are stored as dash as is shown with exiftool:
Country : ---
State : ---
City : ---
Landmark : ---
IMO the camera should show at least the country and state in the land-mark info, Apparently if there is not a POI the camera don´t show anything
I think the panasonic should take note of this for the next firmware update.
I will post the experience if I have the opportunity of check this issue in a big town.