Yes—within the limits of a compact camera, you can improve this. The main issue is that autofocus prefers the reflected subject because it has clearer contrast than the mirror surface.

Try this:

• Focus on another object placed at the same distance as the defect, half-press the shutter to lock focus, then recompose and take the shot.
• Or place a small high-contrast marker very close to the defect, focus on that, and shoot with the marker nearby.

Lighting matters as much as focus. Surface defects show up best when the mirror is lit so the defect scatters light differently from the surrounding surface:

• Use very low-angle lighting across the surface, or
• Use coaxial lighting, which is commonly used to reveal mirror-surface defects.
• A ring light can also help give more even illumination.

So yes, you may be able to do it with the Panasonic if you lock focus on something at the same distance and use lighting designed to emphasize surface flaws. If autofocus still struggles, manual focus would help if your camera offers it.