Is it possible to clear the "back/forward" history of a specific tab? :

You can go back to the earliest entry in the tab and open a new page so that you remove all of the forward history, but you can't remove the original or reduce it to just the original entry in the tab.

App-tabs are pretty much like regular tabs except that the tab is protected from opening a direct link or bookmark to another site within the app-tab -- that does not apply to bookmarks with substitution or javascript as they will open in the same app-tab.

App-tabs provide no more protection than normal tabs against web pages like this one while composing a reply where the typed text is frequently lost during composing and have to start over.

Copy and paste this code in the Code field in the Tools > Error Console and click the Evaluate button to clear the tab session history. This code also works for extensions that allow to run code with chrome privileges (Keyconfig, mouse gestures, custom button, PrefBar).

var Cc=Components.classes, Ci=Components.interfaces;
var os = Cc["@mozilla.org/observer-service;1"].getService(Ci.nsIObserverService);
os.notifyObservers(null, "browser:purge-session-history", "");

That last one worked like a charm. Is there any side effects to this? Other than losing all your session history - rather than a single tab?

Now how to make it into a button would be another question...

PrefBar uses this code in the "clear all history" button to remove the session history.
I do not want to delete all the history, so I've created a button with just this code and never had any problems with it.
I use it to keep tabs and sessionstore.js clean with tabs that I reopen in every session.