It is not a problem with the camera. It is the software you should be concerned with. If your MAC has a photoediting software you will not have any problems. Get a memory card reader and use it to transfer your photo files, there is no need to connect the camera directly to your MAC.
Ya, Berny's right. I have a mac, and if you hook up your camera to the comp, you can set up iPhoto to download the pictures from your camera.
In fact, I have the same camera. I really like the TZ1. As for panasonic offering software, I usually throw out the software that comes with hardware like that. But it does come with software, so not to worry if you don't have iLife. Hope that helps!