that’s not distortion, that’s interlacing.
your video was shot interlaced, 2 separate fields for each frame (look it up)
FCP just shows you one field only, so it looks fine there
computer displays can’t do that, they show both fields at once,
giving you that doubled up look,
and yes, the more movement, the more you’ll see it.
if a computer screen is where the videos are to be seen, you need to de-interlace them in FCP before you export.
FCP has it’s own de-interlace filter, it;s OK.
but Natress G Smart De-Interlace is the best quality de-interlace you can get in FCP.
you can also use the free JES De-interlacer outside of FCP on your exports
if you are making a DVD or going back to tape, then don’t worry, interlaced is acceptable.
cheers,
nick
(and you should upgrade to FCP 7.03)