Have you first - exported a Quicktime movie from FCP and watched it? That would be my first step. Then run that .mov file through Compressor as Constant Bit Rate with settings of not higher than 6 Mbps and not lower than 4.5 Mbps. Once it gets into DVD SP you need to built the VOB files and the Video_TS folder and try it again in Apple DVD Player. If it still looks good there, you can burning it to a disc.
Generally, you may be failing with too high a Bit Rate for that DVD Player causing all those problems on playout.