I've verified that the ISO images I've downloaded are okay: although Mac OS X doesn't have sha1sum installed as a program, it is possible to get that as part of the textutils image from Fink, but even that's not necessary: the openssl program can compute a SHA1 checksum:
$ openssl dgst -sha1 my-image-file.iso
Meanwhile, previous experiences showed that I had lots of problems getting images to verify in this box at last time around: CDs and DVDs given to me by others verified fine on boxen at work but not here, and FC3 failed to write images. But I got away with it (ish) by writing them on the shiny new Mac, last time. That's what I've done this time too, and I'm currently trying to verify them in the DVD drive instead of the CD drive, to see whether that makes a difference. uts666 suggested there were problems with the drives generally, and that I should just buy new ones. While there's something in that, it's not going to be too long before I replace this desktop with an iMac anyway, I think.
 "Ish", because last time, I got all the CDs to verify, then the install barfed on a disc error about four hours in, and I spent many hours trying to figure out what the fuck was wrong with the installation, as a result. Want to bet the same thing will happen this time?