This exposure: aperture f2.8, shutter 1/320, ISO 80, focal length 35mm equiv.
This photo does appear a bit soft to me, I'd like some other Z612 users or users of other Kodak super-zooms to jump in on this.The shutter speed and wide-angle focal length probably rules out camera shake as a contributer. The aperture is f2.8 which is wide open and probably less than optimal. Most lenses clean up considerably at one stop down from wide-open and are closing in on optimal at 2 stops down.
It appears to me that the focal plane was near front edge of the triangular box and back corner was getting to the outer limits of the depth of field which contributes some to the softness.
I applied the IrfanView sharpening filter and it increased the appearance of sharpness in the picture (without adding any detail of course.) When I did this with Steve's wide angle test shot (shot at f4) it had no apparent effect.
If you're really sure it was taking better pictures whenthe camerawas new (and especially if you have a shot similar to this taken in that time frame) it might be appropriate to contact Kodak. They can probably get an idea about the warranty by the serial number.
The dog photo was clearly one that nobody could reasonably expect to be sharp. This one is so much closer that I'm much less sure what reasonable expectation should be so I hope others will jump in to help. I also would still recommend doing Bailey59's test sequence.
Maybe RonBaird can jump into this thread.