28-3-14: As I published it in april 2012 developments kept ongoing of course, that is I way I have a update.
Facebook developers made a WordPress plugin To post posts etc in facebook, with comments to vice versa. Here a more detailed description The Facebook plugin for WordPress adds Facebook social plugins to your WordPress site. Associate your WordPress site with a free Facebook application identifier to enable advanced features such as automatically sharing new posts to an author’s Facebook Timeline or your site’s Facebook Page. This plugin is developed by Facebook with extra support for popular plugins and themes, custom post types, and custom post statuses.
So what is better then use plugin from the facebook makers them self.
It is not the easiest setup.
Make APP in facebook you need developer account
Click the “+ Create New App” button on the top right of your screen to create a new Facebook application.
Then to get wordpress post published on facebook page ( I assume you have one). Go to users in wordpress administrator dashboard, fill in the needed fields.
See following for more detailed instructions.
The Facebook plugin for WordPress supports associating WordPress content with an author’s Facebook profile and optionally posting new content to an author’s Facebook Timeline. A WordPress site may also publish new stories to a Facebook Page if a site author has Content Creator permissionsfor a Facebook Page.
Connect WordPress author accounts with a Facebook account
A site author may associate a Facebook profile with a WordPress account through his or her WordPress profile page (typically found at wp-admin/profile.php). Authors will be asked to authorize your application to access his or her Facebook public profile and friend list to associate authored content with Facebook account identifiers.
An author may optionally grant your application permission to publish new posts to his or her Facebook profile when the post becomes public. Publishing posts to Timeline may be disabled by default for new posts by the author and manually set from the post edit screen.
An author with an associated Facebook account will be granted content moderator permissions on his or her authored posts implementing the Facebook Comments Box social plugin. The author’s Facebook account identifier will be automatically output on his or her posts and author page to enable Facebook-specific bylines and allow people on Facebook to subscribe to future articles by the author published by your site.
Connect a WordPress site with a Facebook Page
Your WordPress site may communicate with Facebook fans and subscribers through a Facebook Page. Your Facebook Page has one or more Facebook accounts with varied roles similar to WordPress pre-defined roles. A Facebook account with content creation capabilities for a Facebook Page may grant permission to your WordPress site (a Facebook application) to post updates to the Facebook Page on his or her behalf.
You may edit the connected Facebook Page for your WordPress site on the Facebook Social Publisher settings page in your WordPress administrative interface.
Select “Allow new posts to a Facebook Page” to grant your WordPress site additional permissions for your Facebook account.
Your WordPress interface should present of list of Facebook Pages your associated Facebook account has permission to create new content. Select a Facebook Page name from the list and save your changes to associate Facebook Page publishing credentials with your WordPress site.
Then the opengraph setup:
So the the below part is obsolete or if you want to you can still use it:
Facebook publish in wordpress can now be done with this plugin. Implementing it in WordPress will save you time in publishing posts. Just do it simultaneously in WordPress, with the use of a tick box.
http://wordpress.org/extend/plugins/facebook-page-publish/. This post is the example.
Also a tutorial on how to implement http://wpvideo.tv/wordpress-blog-posts-auto-feed-facebook-fan-page/wordpress/682/