Staff from Edinburgh City Libraries have been in touch with me, and are investigating what's happened with my missing membership application.
They may have suffered a process fail with the electronic submission procedure, but actually being pro-active and responsive to the issue is a big positive for their customer services. In Mastercard terms:
Form submission not being acknowledged?
No membership card appearing after a month?
Wondering what's happened to your personal details on the missing form?
Spotting the issue and contacting the user?
Plus...they're getting e-books! I finally have a good reason to use the public library: it would give me something I want, in a convenient way!
P.S. - the people commenting on that link in the Scotsman are mad.