The way Tk::DBI::Table currently works, is that the first column selected is assumed to be a primary key, and so it must be unique. If you have no unique columns, then you're out of luck. I have an idea how the module should be patched, but no time to work on it. I've also emailed the author but have not heard back yet.

And to answer your earlier question, no, I can't sort on the first column either.