First , you know how 24p media is supposed to look, right? The motion blur on 24p can be disorienting if you're not used to it. The vibration most likely rules this out, but it doesn't hurt to check.
Could be incorrect field order, or an interlacing issue. Don't trust computer screens for this kind of thing -- computers are blind to issues with interlacing, so you won't see it unless you're using an external monitor. If it looks bad on an external monitor, then that's what it really looks like, and will very likely be like that on DVD.
Try a Shift Fields filter, or Flicker Filter. You should also take one of the clips, open it with FCP, then play it straight from the Viewer into an external monitor. Your original footage may have been converted incorrectly to begin with, in which case you may have to go right back to the source and redo the conversion. Select one of those clips in FCP and press APPLE-9, and list the information there.
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