Thanks for all the help! I've more or less sorted it out. I installed FDshow, even though I probably already had it as part of K-Lite as you said. That helped with some files, but there were still 10 recalcitrant files. They were all wmv files, and when I used Mediainfo on them, I saw that they all used a VC-1 codec. All the wmv files that used WMV1, 2 or 3 were OK. But the strange thing was that some of the VC-1 files thumbed OK.
I then opened FDshow's configuration utility, and I saw that VC-1 was listed as disabled. I assume that means that some other program handled it. I then instead selected libavcodec, and they all thumbed like a dream!