I know my Careers vanity URL is
/pekka because I vaguely remember picking that once.
I see no way to discover it in the actual careers profile, though.
That should probably be fixed.
Edit: ahh, it's in "privacy settings".
It should be more prominent, I met somebody the other day who didn't know the feature existed.
How about putting it in the top of the bar to the right, or place it in a separate menu item labelled "Public URL" or so?