When I render my project to MPEG-2 format, the edges of the moving objects in the video become fuzzy only during moving, once the objects stop, the edges become straight and sharp!. This problem doesn't appear when I render the video to MPEG-1.
Are you sure you have your MPEG1 & 2 straight? Usually this fuzz (known as compression artifacts) is seen in MPEG1 and not so much in MPEG2 if the bitrate is high enough (over 3000 kbps). The problem is that you are running out of bits to represent the image. Images with motion need more bits that images that are not moving. I have never seen this when rendering to MPEG2 using the DVD template because it uses 8000 kbps VBR. What template or bitrate are you using?