1080i is a ATSC video high definition standard. Your X-Box being set to that will help the clarity of the image and make things look, and fit better on your screen. So that is a good thing.
The cautions are that with any gaming system on either Plasma or CRT based products (yours is CRT) is that you have to deal with burn in. That is, if you leave the same image up, or if someting like the words: Player X Score: XXXXX appear on the game, in the exact same place, and you leave it there all day long then there is the possibility that it will still be there when the TV is watching something else.
I do not believe that this is nearly as big of a problem with CRT technology as it is with plasma technology, but it is definitely a possibility.
The biggest thing you want to avoid with your TV is watching a lot of 4x3 content (narrow screen) on your 16x9 (widescreen) television with black bars on the side. At the very least, make the bars on the side gray so that burn-in is reduced.
There is a ton of information online about burn-in and how to avoid it and what causes it. I believe there is also an article or two on Audioholics about it.