Gdm opens a file descripor for logging and then uses dup2(2). However,
the origianl file descriptor opened is not closed. The leak occurs
when a user logs out of X and will continue untill gdm is restarted,
usually when the system is rebooted. I believe this effects all versions of gdm to date. The following patch 
fixes this problem:

diff -ruN gdm-2.0beta2.orig/daemon/server.c gdm-2.0beta2.new/daemon/server.c
--- gdm-2.0beta2.orig/daemon/server.c   Sat Dec 23 17:02:11 2000
+++ gdm-2.0beta2.new/daemon/server.c    Sat Dec 23 17:54:51 2000
@@ -96,6 +96,7 @@
     if (logfd != -1) {
        dup2 (logfd, 1);
        dup2 (logfd, 2);
+       close (logfd);
     }
     else
        gdm_error (_("gdm_server_start: Could not open logfile for display %s!"), d->name);
diff -ruN gdm-2.0beta2.orig/daemon/xdmcp.c gdm-2.0beta2.new/daemon/xdmcp.c
--- gdm-2.0beta2.orig/daemon/xdmcp.c    Sat Dec 23 17:02:11 2000
+++ gdm-2.0beta2.new/daemon/xdmcp.c     Sat Dec 23 17:54:36 2000
@@ -750,6 +750,7 @@
        if (logfd != -1) {
            dup2 (logfd, 1);
            dup2 (logfd, 2);
+           close (logfd);
        }
        else
            gdm_error (_("gdm_xdmcp_handle_manage: Could not open logfile for display %s!"), d->name);