First I have to say that I get the impression that the program doesn't really crash, but simply closes due to some error in the default action linked to pressing the Enter key.

I tried to follow the instructions and didn't really succeed. I'm not sure I was doing it correctly. Here's what I did, maybe you can find what I did wrong:
Installed the gnome-panel-dbgsym package, navigated to
/usr/lib/gnome-panel/
and from that location I ran gdb. Here's the outpou of the first try:

############################################################################
oren@lucky:/usr/lib/gnome-panel$ gdb gnome-clock-applet-mechanism 2>&1 | tee ~/gdb-gnome-clock-applet-mechanism.txt
GNU gdb (GDB) 7.1-ubuntu
Copyright (C) 2010 Free Software Foundation, Inc.
License GPLv3+: GNU GPL version 3 or later <http://gnu.org/licenses/gpl.html>
This is free software: you are free to change and redistribute it.
There is NO WARRANTY, to the extent permitted by law.  Type "show copying"
and "show warranty" for details.
This GDB was configured as "i486-linux-gnu".
For bug reporting instructions, please see:
<http://www.gnu.org/software/gdb/bugs/>...
Reading symbols from /usr/lib/gnome-panel/gnome-clock-applet-mechanism...Reading symbols from /usr/lib/debug/usr/lib/gnome-panel/gnome-clock-applet-mechanism...done.
done.
(gdb) handle SIG33 pass nostop noprint
Signal        Stop	Print	Pass to program	Description
SIG33         No	No	Yes		Real-time event 33
(gdb) set pagination 0
(gdb) run
Starting program: /usr/lib/gnome-panel/gnome-clock-applet-mechanism 
[Thread debugging using libthread_db enabled]

** (process:31912): WARNING **: Failed to acquire org.gnome.ClockApplet.Mechanism: Connection ":1.132" is not allowed to own the service "org.gnome.ClockApplet.Mechanism" due to security policies in the configuration file

** (process:31912): WARNING **: Could not acquire name; bailing out

Program exited with code 01.
(gdb) exit
Undefined command: "exit".  Try "help".
(gdb) quit
############################################################################

So I tried the same thing with sudo, but that didn't seem to work either:

############################################################################
oren@lucky:/usr/lib/gnome-panel$ sudo gdb gnome-clock-applet-mechanism 2>&1 | tee ~/gdb-gnome-clock-applet-mechanism.txt
[sudo] password for oren: 
GNU gdb (GDB) 7.1-ubuntu
Copyright (C) 2010 Free Software Foundation, Inc.
License GPLv3+: GNU GPL version 3 or later <http://gnu.org/licenses/gpl.html>
This is free software: you are free to change and redistribute it.
There is NO WARRANTY, to the extent permitted by law.  Type "show copying"
and "show warranty" for details.
This GDB was configured as "i486-linux-gnu".
For bug reporting instructions, please see:
<http://www.gnu.org/software/gdb/bugs/>...
Reading symbols from /usr/lib/gnome-panel/gnome-clock-applet-mechanism...Reading symbols from /usr/lib/debug/usr/lib/gnome-panel/gnome-clock-applet-mechanism...done.
done.
(gdb) handle SIG33 pass nostop noprint
Signal        Stop	Print	Pass to program	Description
SIG33         No	No	Yes		Real-time event 33
(gdb) set pagination 0
(gdb) run
Starting program: /usr/lib/gnome-panel/gnome-clock-applet-mechanism 
[Thread debugging using libthread_db enabled]
** (process:31920): DEBUG: Setting killtimer to 30 seconds...
** (process:31920): DEBUG: Exiting due to inactivity

Program exited with code 01.
############################################################################

I then tried to manually activate the clock settings program after running gdb and that didn't create a backtrace either:

############################################################################
(gdb) run
Starting program: /usr/lib/gnome-panel/gnome-clock-applet-mechanism 
[Thread debugging using libthread_db enabled]
** (process:31923): DEBUG: Setting killtimer to 30 seconds...
** (process:31923): DEBUG: Exiting due to inactivity

Program exited with code 01.
(gdb) backtrace full
No stack.
############################################################################

at that stage I tried to work according to the "Already running programs" part of the manual for creating a backtrace, but I was unable to identify which process I was trying to follow. Then I pretty much gave up :)
any ideas on what to do now would be welcome.