After you rendered the video in the RM, did it look good or bad quality?
See, that's just the thing. I got smart and opened the reply video on a 1080p (ish) monitor and it looked great! So that leads me to lean toward it being an exporting fault in FCP.
But I did have one question. Zemunsta, or anyone that exports videos that look good - do you select MP4 high quality in the replay mod? Or set the bit rate yourself?