Thanks, Digital Guru, I think you've earned that tag. I'm dying to know if your suggestion works and will try it ASAP. In the meantime though, I gave the problem DVD (which was itself a copy made by someone else) to a friend to see if he might be able to copy it. He got the same message (that the video was damaged).
I talked with the person who made the copy (In England, but it's not a regional problem) and he had copied it from a download. It plays perfectly, which is what puzzles me.
Will let you know if my friend is able to copy it. I've also forwarded your suggestion to him, should he need your Guru vibes.