jasonw,
As I mentioned in post #2, you can exclude the desired holes from the Clipping Mask by creating the Compound Path, then use that as the Clipping Mask.
Working with raster images, as is clearly the case here, has its limitations.
Obviously, the parts hidden by the Clipping Mask are still there.
You could remove parts of the image inphotoshop, if you also have that, or you could Image/Live Trace the image so you get a vector rendering of it, which can then be reduced to the parts you want.
If you wish to get rid of the parts of the raster image outside the Bounding Box of the Clipping Path/Mask, you can do the dirty destructive deed, with the Clipping Mask selected:
1) In the Transparency palette/panel dropdown list select anything but Normal (Multiply is fine; this step may be unneeded in your version, you may try;
2) Object>Flatten Transparency, just keep the defaults including 100% Vector;
3) Shudder.