How do I enable push notifications for Facebook for Android?
Funnily enough, as I just noted here I believe that the app is just buggy and unreliable.  There's no reason for the individual device to determine whether the application can do something like push notifications.  Android's cloud to device messaging requires 2.2 or higher, and the Facebook post notes that that's what they require as well, so I assume that's what they're using. C2DM works perfectly fine for other apps so the only reasonable explanation is that the Facebook app doesn't work properly.

The app was updated recently and does work better for many users, though, so make sure you have the latest version.

There are no settings related to push messages in the app or in the Accounts and Sync settings.  Regular sync is every 3 hours at most, which seems infrequent to me &mdash; my BlackBerry allows updates every half hour.