Thank you for posting this problem. With issues like this is is hard enough knowing how to describe the problem that will make sense - but stationary grain describes it complelety.
I burnt a DVD for a project yesterday - and put it in my DVD player just to check it works and was shocked at what I saw: horrid noisy image with grain. Particularly on black frames.
I tried different compressor settings everything was horrid.
Reading the posts today I exported a master 1080p clip. Closed FCPX 3. Archived it. Un-archived my last copy of FCPX2. Created a 1080p timeline. Dropped the clip in then clicked 'burn DVD'.
At this point I always find the encoded files (hidden in the FCPX Library Bundle) and copy them to use in the now archaic but still very useful DVD Studio Pro. (Lets face it the DVD menu options in FCPx are such an embarrassment.)
I added the encoded files and burnt the disc. This time... No stationary grain. The problem has to be FCPX 3. Something has been changed - it is not in the release notes but something is different. Apple please sort this out.
I've wasted half a day trying to find the problem. And now I have to do switch backs between two programmes when creating DVDs.