Sadly, most information in this thread is wrong. Balls got it right, Windows 8 has the same issues, btw.
Facebook chat in the Messaging hub is worthless. It's the same thing on Windows 8. If the Hub is open, it seems to work fine while you're in it. However, when it's closed there are tons of issues with missed notifications or missing messages in the thread. This also happens in the Windows 8 Messaging Hub, FWIW (been experiencing it since launch).
The WP FBC issues are as old as the FBC integration itself. It has ALWAYS been broken, literally. It's part of the reason why I went back to Android following Mango release. As I moved most SMS to FB Chat Windows Phone made it impossible to efficiently communicate with the people I talk to.
Also, Microsoft integration/app does not keep pace with Facebook Messenger. No Seen tags or picture transfer.
Old issue. Always been there. Doubt it will be fixed soon, if it's apparently still there now. Yes, it's a pretty embarrassing issue for them, IMO, as the FBC integration was a huge selling point but turned out to be too much of a hassle to be worth it - given FB is not developing for the platform.