There some applications which I can not yet run in full-screen mode. I particularly would need the OSX Terminal app and possible the TextEdit. However, after the upgrade they remained the same, and does not have the full screen button in the top right corner. How can I enable Lion style full-screen mode for there applications?
Another terminal like application is iterm2. It goes fullscreen and works extremely well!(a lot better than terminal)
Lion's Terminal.app does support fullscreen mode. Maybe you are overlooking it? How did you upgrade?
As for TextEdit, applications need to explicitely implement Lion fullscreen support, and this has not been done for TextEdit. There are other 3rd party text editors that have implemented fullscreen mode, depending on what usage you have for a text-editor.
Terminal does support Full Screen on Mac OS X Lion. It sounds like you’re opening an older version of Terminal. Check Terminal > About Terminal to see what version you’re using. It should be 2.2 or later.
You can see the location of the Terminal you’re using by Command-Clicking on the Terminal icon in the Dock. That will reveal the Terminal application in Finder. It should be in
/Applications/Utilities/Terminal on your startup volume.