I had a similar (albeit much more lo-fi) problem when trying to import some football (soccer) footage into FCP that I’d originally made with iMovie / iDVD. I tried Cinematize Pro, and also importing from the original DVD into iMovie and FCP via a DVD recorder/player with Firewire and all of them showed jagged lines and shadows for the faster motion parts, presumable due to interlacing and maybe the relativley low bit rate used by iDVD to make the original DVD.
But using MPEG Streamclip, File, export to DV, defaults and ticking “Deinterlace Video” got rid of the annoying jagged lines and shadows.