This is probably due to a piece of dust on the IR filter inside. There's an excellent video on youtube (https://www.youtube.com/watch?v=0nmwt0frZns) by Graham Houghton which shows how to remove it. I did this three times on a TZ-10 with 100% success and 0% damages.
Since the dust is not on the sensor, but 2 mm away on the filter, a closed iris and a light detail free picture (like cloudless sky) is the best way to watch these spots.
Another hint: The spot will not move with various focal lengths (zoom), but you'll see it moving when the cam switches from optical to electronical zoom (if enabled).