The footage Sam has imported on his computer is in high definition, and DVDs aren't capable of playing back HD content. It also could be an interlacing issue. If his footage looks like it's being viewed through window blinds, he should find software that will de-interlace the video. If he wants high definition, he'll have to author his videos to Blu-ray discs.
Ultimately Leo recommends watching the video on his computer since DVDs don't have much of a future anymore. He should make sure to keep backups of those videos too.