Microsoft has quietly released version 2.0 of its Facebook app for Windows Phone. The biggest improvement is undoubtedly the addition of Push Notifications. You can now turn on toasts and/or a live tile count for the notifications.
If you've got the Windows Phone Marketplace live tile pinned to your start screen, you should have already gotten a notice that an update is available. You can download the new version from this link: Facebook for Windows Phone.
The Push Notifications feature is very easy to customize. You can choose to be notified about a new Message, Wall Post, Feed comment, Feed comment reply, Photo tag, Photo comment, Tagged photo comment, Photo comment reply, and so on. All of those are optional notifications, meaning you have complete control over what the app notifies you about.
Other than Push Notifications, I'm not sure what else is new. The app reportedly feels a lot smoother, but that's all I'm hearing. I have contacted Microsoft for an official changelog and I'll update this post if a spokesperson decides to reply with something tangible.