Here it is in nicm@'s words:
"In particular, being able to share a single window between multiple terminals, with other windows in the same session but entirely separate. Adding this to screen was implausible"
Perhaps I am still misunderstanding the features of tmux (most likely in fact), but to say that is implausible to add to screen is misleading to say the least, since I have been doing exactly that in screen for nearly a decade.
On one terminal, either start a new screen session or -r to a detached session.
If starting a new one, try: screen -S LetsShare
On a second terminal, run: screen -list
You should see a list of screen sessions and their status (attached, detached, multi, etc)
If you used -S on start that will be the name, otherwise it's some tty.host.number string.
Now on that second terminal run: screen -x
Try to adjust both terminal sessions so you can see them at the same time. Type in either, watch in either. They are shared seemingly matching your tmux description.
You can change permissions per terminal so others can't type but will see everything you do (aka tutorial mode) using ^a *
Also for split/multiple windows showing on the same terminal, use ^a S (control-a capital-S)
To switch between split windows use ^a tab
Close a section of split window with ^a Q
The status bar problem is true and pretty annoying. I fixed it myself with a line in ~/.screenrc but of course I have to pretty much install that user config file on every new system I use which can get annoying.
If you want an always-on status bar showing window numbers and titles (^a A to change the title), add this to .screenrc (and hope slashdot doesn't munge it!)
hardstatus alwayslastline "%{= wk}%-Lw%{= BW}%n%f* %t%{-}%+Lw %-=%{= BW}%H%{-}%{-}"
Note the two "BW" bits? That's background blue and foreground white, and applies to the window with focus. Change B to R for red for example (production vs not-production in my case)
Here is my whole .screenrc file for copy/paste purposes: http://pastebin.com/kMkuFXi9
No splash screen, always on status bar, 10k line scrollback history for copy/paste (^a [ and ^a ] ), and auto-open three windows with preset titles and commands running in them.
I don't mean to knock tmux in any way at all, having not used it (and I do plan to check it out now) - but hopefully these screen tips help out others here.