If you have a standalone TiVo, any video you watch from it will definitively be worse than the source, since it's using MPEG (2, I believe) video codecs to compress it lossfully. In most cases, it's not much worse, but it is noticeable when you first switch over. Once you use it for a while, you probably won't notice it any more except the rare occasions when it gets bad. Rippling water and video static are two such instances that it has a hard time dealing with. "Any video" includes even "live" TV when you watch it via the TiVo. In order to give you the slomo, pause, etc., it actually records live TV and replays it a few seconds later. If it annoys you for whatever reason, you can also bypass the TiVo and plug your initial source directly into the TV as well as into the TiVo. Then you can switch TV inputs to see real live TV, sans video compression.

It's important to point out that you should only run your live TV source(s) through the TiVo and make sure other things like DVD players don't run their video through it. It'll compress the video making it worse without providing you any benefit (not to mention that pressing play, pause, etc. will all be delayed by the few second TiVo live TV buffer), and that's provided that the TiVo won't do weird things with Macrovision, which it may.