Does this not work for you?

From http://www4.informatik.uni-erlangen.de/~jnweiger/screen-faq....

  Q: My xterm scrollbar does not work with screen.
  A: The problem is that xterm will not allow scrolling if the
     alternate text buffer is selected. The standard
     definitions of the termcap initialize capabilities ti and
     te switch to and from the alternate text buffer. (The 
     scrollbar also does not work when you start e.g. 'vi'). 
     You can tell screen not to use these initialisations by 
     adding the line termcapinfo xterm ti@:te@ to your 
     ~/.screenrc file.

No, it becomes chaotic and unusable when I have more screen windows and switch among them :-)

I would not complain, if I knew such an easy way to make it work, really. :-)

"Ctrl-a [" will put you enter the copy buffer mode and let you scroll up

Sure, but that's only a poor substitute. I can't just press shift + pg [up,down] or drag scrollbar in the terminal emulator or use mouse wheel.

Yeah I know, Shift+PG[up, down] not being usable is kinda a bummer but as a bonus you can use / to search the scrollback buffer plus all the vi movement keys are available.