What's interesting about the Mozilla blog and the video is that it shows how the full-screen browser will work on a smartphone: you can move to the side to zoom out of a page, and you can access forward and back buttons by moving to the left, but for the most part the entire browser runs without any, er, chrome [that is, address bar, status bar] around the content. It looks a bit like the iPhone browser but will have the one distinct advantage of being available for just about any phone.
I have always preferred full-screen browsing, although it's cumbersome on the desktop because there are no actual controls for full-screen mode, unless you know keyboard shortcuts. On the desktop, a true full-screen browser would have options for quickly accessing forward and back buttons, bookmarks, search, and other options by moving your mouse to the side or by some other method. The idea of highlighting the content - especially important for Web apps - makes sense on the desktop and on phones. (I know that developers can present apps in full-screen mode, and I know Chrome has a mode where you can get rid of the handlebars as well, but it is still cumbersome to find browser buttons and options.)
I think Firefox Mobile is onto something, and points to a future of computing where screen interactions are more kinetic. There is more movement than just scrolling up and down.
It turns out that Microsoft agrees. Several projects are underway, which I will be reporting on at another IDG outlet soon, that use new computing paradigms like the one Bill Gates demoed at CES this year (called the Touch Wall). The Touch Wall interface, called Plex, reminds me of Firefox Mobile. This is all likely a precursor to Windows 7 or maybe Midori and finally achieves the vision for multiple windows in a freeform environment - an "interfaceless" operating system that consists of smart objects you can move and manipulate on the screen.
And where is this all heading? I think, once the browser and the OS become nothing more than smart objects, computer paradigms will finally shift from being tied to a PC. The OS can exist on any screen - your bathroom mirror, the window on a car, a table, the wall outside your home. This kind of interface will be pervasive - and obviously Web enabled. (But it probably won't be a Microsoft or Google OS.)