Patch for Mac OS Emacs 24.3rc3,
now for historical interest only: 27.1 is better
(and can be installed on older Macs via MacPorts' emacs-mac-app)

On 2013-03-15 I submitted this patch to
http://debbugs.gnu.org/cgi/bugreport.cgi?bug=13840
One developer said this patch is incorrect; another said
the problem was fixed in trunk.
The release of 24.4 indeed fixed the bug, but 24.4 also
introduced a new bug when used with Mac's Zoom function,
reported to http://debbugs.gnu.org/cgi/bugreport.cgi?bug=18833
on 2014-10-25; also http://comments.gmane.org/gmane.emacs.aquamacs.devel/992
24.5 still had zoom bug although it was less serious because the
mouse needs moving only 1 pixel more to pop up the correct menu.
That was still the case in 25.1 (hold down mouse while moving a pixel).
Bug became more serious in 25.2: clicking to the right of the
menu bar can sometimes lock up Emacs.  Still present in 26.1.

All relevant bugs completely removed by 27.1 (mid-2020, see above),
which finally let me stop using 24.3rc3 with this patch on an old Mac.

Old patch:

This patch was tested on emacs-24.3rc3, do:
patch src/nsterm.m < patchfile
./configure --with-ns
make install

--- emacs-24.3/src/nsterm.m~	2013-01-04 09:38:13.000000000 +0000
+++ emacs-24.3/src/nsterm.m	2013-03-15 11:29:10.000000000 +0000
@@ -3461,7 +3461,7 @@
       if (writefds && FD_ISSET(k, writefds)) ++nr;
     }
 
-  if (NSApp == nil
+  if (NSApp == nil || apploopnr != 0
       || (timeout && timeout->tv_sec == 0 && timeout->tv_nsec == 0))
     return pselect (nfds, readfds, writefds, exceptfds, timeout, sigmask);