The FF4 delivers an app tab feature and it looks like both Gmail and Twitter have some notification code when a new mail or tweet come the app tab would look like a litter lighter. Does any know how to operate the app tab with the notification? I can see the code of a pinned application of IE9 with similar function. But I could not run into any document of FF.
Do you mean that you're building a website and you want to let Firefox notify the user on an event when the tab is pinned?
I'm fairly certain Firefox does it when the website's <title> is changed. For instance on Twitter, when there's a new tweet, the title is changed from "Twitter / Home" to "(1) Twitter / Home". Firefox notices this and notifies the user.
So really, any javascript function that changes <title> will make it work.
I hope that helps