Well, the P&S is dead, and no batteries. So I have attempted to replicate using my big cam with a macro lens. Heh.
The way I see it, the camera is selecting what it thinks might be the best point to focus on. Without getting into the complexities of how it selects, and high/low contrast, lines, color, etc (which I don't really understand, but I know that's part of the selection algorithm,) let's just say that sometimes the camera picks the wrong part. Poppet will help demonstrate:
In the first image, I have a shallow DOF (F2.8 at 100mm,) and I've used my spot focus, which I can half-depress the shutter to get the focus directly on her face, then recompose. You can see that very little other than her face is in focus.
In this image, I've let the camera choose the focal point for me. For some reason, the camera liked her wing, not so good.
While a shallow DOF has its artistic merits, as important as knowing HOW to use it, is knowing when NOT to use it. In this case, I wanted to get more than just her face in focus, and the only way to do that is to use a smaller aperture (larger f#.) In this case I used F5.6, which was enough for such a small object. At this DOF, even the tip of her little magic wand is now in reasonably good focus, while her skirts have just a little bit of bokeh (blur) to keep it from looking like an ebay shot.
Let's see it with tea:
Here, the camera liked the leaf in the front, the pile is in poor focus.
Now the camera auto selected the back of the pile. Hmmm... Do Not Like.
In this one, I used spot focus to choose where I wanted the focus: front middle of the pile. Better.
Last, I used more DOF to get more detail of more leaves, which seems to work the best for this kind of example.