Yes, you will need the dvds either in the normal DVD folders and VOB files, or as a straight ISO rip for LMCE to play them....
As for the green flashes, don't know, never seen them - perhaps try playing the converted files back on the KDE desktop using Xine Player. Whilst LMCE doesn't actually use the Xine Player UI, it does use the underlying libraries and codecs, so if you see the same behaviour then you can assume the problem is in Xine's code/codecs and try to track down the bug upstream. Are you using 0810? Also bear in mind not every group's interpretation of a compression or container standard is the same, and so Xine maybe playing back just fine, just the transcode wasn't as good as it could be - and yes, just because WMP or some other player doesn't exhibit the same behaviour doesn't prove that the transcode isn't at fault, they may just be more tollerant of such transgressions. It would be worth using 1) another transcoder and 2) a different codec.