OK. Progress has been made. It wasn't the line endings, per se, but rather some garbage apparently being added to some lines. I had been using Padre since taking up Perl a couple of weeks ago. After your comments, I loaded the offending file into Textpad, only to observe that the problem persisted and that the line endings looked OK (with "view whitespace", anyway). In a rare moment of lucidity, I saved the file and reloaded it; and the problem was gone! My Textpad is configured to "strip trailing spaces" when saving. So some extraneous content, invisible, apparently existed on random lines. Perl is off the hook.
This probably also explains some strange error messages that I've had, which were only resolved by deleting and retyping the indicated content with what was visually identical content. So Perl is off the hook for that, too.
Thanks guys. I probably should have thought of cleaning up the line endings earlier, but I didn't until prompted. Now I'll be looking for a different editor (Win 7 64-bit).