First and foremost - No, you will have no issues with legacy equipment in this brilliant age of 1080p. All current 1080p sources can be played at lower resolutions which typically include 1080i, 720p, 480p, and 480i.
For your display... it doesn't matter what the native resolution is. People above are confusing the issue, but we will discuss it anyway.
It seems a lot of people don't realize that when 1080p displays first hit the market, the microchips necessary to process 1080p sources did not exist in vast supply. So, they hobbled together some chips that could convert 1080i, 720p, 480p, and 480i to 1080p resolution for their new 1080p displays. The general public didn't care, or notice as all the sources on the market were NOT 1080p.
Step forward a couple of years and you now have 1080p displays which all accept 1080p resolution as well as 1080i, 720p... etc. If you have your ear to the ground on displays, a 'new' term related to 1080p is the ability to handle both 60hz source material (1080p/60) and 24hz source material (1080p/24). This is actually something that I've been expecting for the last 3 years since Blu-ray was announced.
klix58 - Rest assured that you will have no NEED to upgrade your display. A 61" DLP is still perfectly capable of handling all the standard HD resolutions up to 1080i... It will CONVERT those resolutions to the native resolution of your display. Actually, since you don't know the native resolution of your display, and you didn't provide a model number, it's impossible for us to know if your display is 1080p, 720p, or something else. It is most likely that your display either has a native resolution of 1280x720 (720p) or of 1920x1080 (1080p) achieved through wobulation.
Does it matter what your displays native resolution is? Maybe. But, for this conversation, it does not. There are several articles relating to resolution vs. seating distance available on this site and online if you want to dig into that as an excuse for a system upgrade.
Also - do your homework on the HD DVD vs. Blu-ray debate before purchasing any players - if you haven't already.