|Zoomed-out to wide angle, the Lumix TZ1 delivers reasonably sharp results in the corners, but zoom all the way in and the results become quite soft. This isn't surprising though for a lens with a 10x optical range that's squeezed into a compact body, and it's important to note the Fujifilm S9500 / S9000 with its considerably bigger optical system also suffers from softness when fully zoomed-in.
Ultimately it's the price you normally pay for the convenience of a very long optical range.
If you want pin sharp results in the extreme corners throughout the range, you normally have to go for a lens with a shorter optical zoom. There are exceptions though, such as the Panasonic FZ30, which delivers sharp corners throughout its optical range; again though, this is a larger camera, comparable in size to the Fujifilm S9500 / S9000.
Note: crop details which appear smaller here are
due to them being captured with lower resolution cameras and / or a lens
which couldn't focus as close to the chart. In each case though, the crop
still represents the extreme left corner of each camera's frame.