so that picture will never be optimal.
DVD is not hi def either so pick up a Blu-Ray player. (Or a PS3 if you play games as that can handle both).
I'm not familiar with the Tivo hardware so I don't know what resolution they pump out but make sure you are getting all your new TV is capable of. (if it's not a HDMI cable or component cables, it's not hi def - the red/white and yellow cables are composite cables and do not send HiDef to your TV)
And do adjust it like suggested in the other posts - here are some links that might help:
http://www.pcworld.com/article/157131/how_to_finetune_your_hdtv.html
http://www.consumerreports.org/cro/electronics-computers/news-electronics-computers/how-to-finetune-your-hdtv-306/index.htm
http://reviews.cnet.com/basic-hdtv-tips/
Full disclosure: I don't have a big flat panel TV yet. I do have an HDTV but mine is about 6 or 7 years old - it's a TUBE TV! Only 30something inches - the biggest HiDef Sony tube tv made at the time. The thing takes up half my living room. I love the picture on it though - it's gorgeous but the damn thing is a behemoth. My friend just recently got a 60" flat panel though and I like going to his house for tv watching. If my Sony will ever die I'll replace it with a bigger screen size but I'll still reclaim several sq feet of living room
by wall mounting a flat panel.
And my apologies in advance if you've already done all that - I didn't see it specifically mentioned so I just wanted to make sure.
Also never spend more than a couple bucks on HDMI cables. I don't care what anyone says, you gain nothing spending 60~80 bucks on Monster cables. Monoprice.com has them all day for 2 and 3 dollars - maybe a little more if you need a really long cable.