I recently updated my Cygwin64 installation.  I've been using the
32-bit version for a while, apparently, but my Setup program for that
wasn't working, so I switched over to the 64-bit version instead.  As
such, I'm not sure if this issue is primarily due to running under
cygwin64, or to having updated versions of the various packages.

Simplest way to reproduce is this: run 'screen', then run 'vim', then
exit with ':q'.  My bash prompt is now on the bottom line of my mintty
window, but everything I type, and all output after that, stays on the
last line, each line overwriting the previous.  Using 'clear', or
switching to another screen window and back with Ctrl-A commands,
fixes the problem.  If I run vim without screen, then it restores the
previous window contents after vim exits.  This always happens with
empty files; it sometimes happens when editing other files, but it
doesn't always, and I haven't tried it extensively to try to figure
out why.

On my 32-bit version, I note that vim under screen doesn't clear the
window when it exits, but it does scroll the window contents up
properly when displaying the bash prompt afterwards.  (It does clear
the window when not running under screen?  Why is that, and is there a
way to get better control over whether vim clears the screen or not on
exit?  Just an aside...)

I copied the .minttyrc file (optimized to put my Cygwin window in just
the right location with just the right size on my second monitor at
work) from my cygwin32 home directory to my cygwin64 home directory,
so it's using the exact same settings.

Attached are cygcheck output from my 32-bit and 64-bit installations,
and my .minttyrc.