error Couldn't open "path-to-file.part": Permission denied

I have since deleted the offending file, forced a verify and all is well so far. Nautilus showed a padlock indicating that the permissions were wrong - how would that happen?

Unfortunately, in my enthusiasm in locating the probably cause of the fault, I deleted it without checking the permissions.

All seems ok.

I suspect the file's permissions were the real cause.

Only one file had incorrect permissions. I suspect/guess that I may have started Transmission as root for a few seconds, and this must have been the file that was created during that time.

But, could the program continue to work on other files and provide a warning instead of stopping?

Problem resolved and not a bug. But I asked whether the error handling behavior could be changed.

"But, could the program continue to work on other files and provide a warning instead of stopping?"

That would probably not be a very good design choice. If some files cannot be written to, there is no reason to believe that the user wants the torrent to continue downloading at all--perhaps the user neglected to set restrictive permissions on the other files, for example. Furthermore, often the user might not want to waste resources like bandwidth and disk space downloading parts of torrents which cannot actually complete due to a problem on their machine. If the user wants it to continue downloading, they can fix the problem. (This is different from a torrent that has fewer than one distributed copy; in that case, network conditions could easily change to make it possible for the torrent to finish, and since this is largely outside the control of the user, there is no reason to assume that the user doesn't want the torrent to continue.)