If you're using Messages to connect to Facebook, you're likely seeing this kind of error..
Every time you put the password in, it says it can't log in and keeps asking for the password over and over. In fact all authentication requests to the old Facebook Chat API are failing now.
So what's the solution? Well there really isn't a very good alternative now if you want to have a chat client that lets you combine several chat accounts into the one app. Sure the Messages app will work with Google Talk alongside other Jabber/XMPP clients, AIM and several others, but it won't do Skype or Facebook.
I had a look around and there are a number of new apps that support just the new Facebook chat. These include Messenger for Mac, Goofy, Astro, Messenger for Desktop, Current and many others.
All of these apps look more or less the same because they are just wrappers around Messenger. None of them offer anything other than connecting to Facebook Chat. To me this immediately disqualifies apps like Current. Why would I pay for an app that does exactly the same thing as another app that's completely free?
So for the time being I chose to go with Goofy...
The look and feel is very similar to the Messages app, but of course it only works with Facebook. It's simple to use, just log in with your email address or mobile phone and password and you're set. All your message history is downloaded automatically. Stickers work. It feels exactly like chatting on the Facebook page, but in an app on your desktop.
The bad thing is it's yet another app for messaging.
So now between my corporate IM client, the customer's IM client and Goofy, I have 3 different messaging apps. Not ideal and hopefully Adium will be updated in the future to support the new Facebook features. I won't be holding my breath though since this feature has been requested 5 months ago and has had no real traction.