The most likely cause is dust or debris on the camera’s image sensor (CCD), not dirt on the outside of the lens. Sensor dust often appears as a dark, soft-edged spot and can be more noticeable depending on zoom/aperture behavior and the scene.

The first step is cleaning, but on a compact camera like the DMC-ZX3 this is usually not a simple DIY job. Reaching the sensor often requires deep disassembly, and community experience with this model suggests the internal plastic construction is fragile and easy to misalign or damage. That can lead to stripped screw mounts, incomplete cleaning, or focus problems afterward.

So the practical advice is: have it professionally cleaned if the camera is worth the cost. If a proper cleaning does not remove the spot, then the sensor itself may be defective and would need repair or replacement. In short: it’s probably sensor dust, not an external lens mark, and self-disassembly on this compact is risky.