Screen door is the space between individual pixels that you see. If you have an incredibly high resolution - say 1920x1080, but it has large gaps between those pixels, you will see the screen door effect even if you feed it perfect 1920x1080 material.
So, do you see the screen door, or do you see the individual pixels and have pixelization issues?
Quite often the answer to screen door is to get further away from your screen. You should not be closer than 1.5 times the width of the screen while watching HDTV, so if you have a 80" wide screen, you should be no closer than 10 feet. But, with DVD and the lower resolution of your screen, you should be a little further away for optimal resolution detail. The added distance helps to make the screen door effect disappear as well as pixelization.
My opinion is that upconverting DVD players are a scam. A good progressive scan DVD player is the way to go when you want the best video off of a disc. The disc doesn't have 720p or 1080i on it - it has 480i. If you upconvert to 720p, your projector just brings it back to 480p. Send it 480p and it should produce about the best image you can hope for.
Not sure of the size of your screen, type of screen you have, or the viewing distance you are at though, so this is all stuff I have just noticed when working with front projection.