OK I made some tests, the conflicting plugin on my site is Simple Facebook Connect.
In the plugin, I have activated the following components :
Publisher (send posts to Facebook)
Allow FB Login to Comment (for non-registered users)
Integrate FB Comments (needs automatic publishing enabled)
Do you think you can find a workaround to allow your plugin and this one work together, or should I begin searching for another plugin for my Facebook communication ? (I want to keep yours absolutely, it's very useful !)