I've just discovered that the frontend "Edit" links are showing for all my visitors, none of them are logged in.
I have worked around this issue for now by hiding all table captions in the CSS.
I'm using shortcodes to display the tables, and the setting "Yes, show an "Edit" link to users with sufficient rights near every table on the frontend." makes no difference On or Off: The "Edit" links are still there.
Also, my WordPress installation is not using any cache plugins, and I have cleared my browser's cookies and cache - the problem remains.
WP-Table Reloaded (DB): 1.9.1
WP-Table Reloaded (Script): 1.9.1
Plugin installed: 2010/10/09 21:04:46
mySQL (Server): 5.1.53-log
mySQL (Client): 5.0.51a