I was wrong apparently in that it appears to be a problem with my burning process. It works if I use the RootsMagic burner instead of my regular one. (Or so it seems - one mustn't jump to conclusions. ;-)
That's a relief. I should have known RM would't have such a big hole in it.
Back again. The trouble returned, but I think that there is some interference between the RM installed on my computer, on which I created the CD, and the CD itself when I test it on the same computer. When I test the CD on another computer without RM installed it works fine. I also note that when I test the CD in the computer on which I created it, its toolbar icon set is different from that on a different computer. Definitely some sort of interaction. Sorry to bother you, but I do like things to work, and if they don't I want to get to the bottom of them. ;-)