OK, I think I'm finally there; WordPress 1.5 is properly installed. It was a bit more tricky and nerve-wracking than I'd hoped, but I think that's probably because I'd done quite a bit of hacking of my index.php and comments.php, so I had to merge the old files with the new changes. However, the new structure for templates should make it much easier to upgrade in future.
It didn't help that I had a corrupted download of the files, permissions problems when I uploaded and conflicts in my .htaccess file. Oh, and a conflict with one of the plugins (HashCash), which is why I made all those cryptic and pointless comments on the previous entry. Anyway, WP 1.5 is a really nice upgrade (and fully justifies the 1.2 -> 1.5 leap). The changes to the admin interface are really smart and make it much easier to manage posts, comments and plugins. As usual, if you do find any lurking problems that I haven't spotted, let me know.