I remember having some issues with the aspect ratio jumping around on my set. I have a 6167 (the 720p native resolution) and I leave my picture setting to 4:3 (not the 16:9 setting that stretches a 4:3 broadcast to fill the screen). When an HD channel is selected, it automatically kicks it over to 16:9, and fills the entire screen. Most non-HD and even some digital cable channels look crappy on the 61" screen, however, the HD programming looks stunning. Additionally, you might still see some horizontal black bars at the top and bottom of some widescreen DVD-movies. This isn't a TV problem, but relates to the aspect ratio that the film was originally shot in. These black bars will be nowhere near as thick as viewing them on a 4:3 TV.
I have a Motorola DCT6200 HD cable box, set to 720p output with a DVI to HDMI cable. If you have component outputs on the TIVO, you might want to try them instead of the S-Video connection. All things being equal, the component cables provide a better picture than S-Video.
Currently, to my knowledge, there are no HD signals being broadcast in 1080p resolution. The TV should handle the conversion from a 1080i or 720p signal transparently. Additionally, I'm not sure about any production DVD players that upconvert to 1080p either. I have a Denon 2910 DVD player set to upconvert to 720p. Unfortunately, the upconverting can only happen with the HDMI cable and since the TV only has one HDMI input, I had to get a switcher to allow simultaneous HD cable and DVD connections.