Start a screen, and have at least two windows in it. Get a different views of the screen by running screen -x from another login (to the same account of course). Make sure that this view is showing a different window in the screen. Type something in one view, then switch to the other view and press UP. Nothing will happen, but if you go back to the first view you will see that UP has been pressed there instead. Doing something other than pressing UP or DOWN in the new view seems to fix this problem. I have only confirmed that this happens (on two different machines, though) when logging in via ssh.
Confirmed. What I'm guessing actually happens is that just hitting up or down doesn't cause sceen to switch to whatever screen is 'foreground' on the current vt/pty/whatever you want to call it.
Fixed in screen-3.9.5, in Raw Hide.