Is this problem still reproducible in more recent versions of Konsole?

  Perhaps. Almost all KDE applications crash once or another time on quit. It is usually not possible to reproduce the same backtrace. Those errors tend to occur in longer sessions. Sometimes on shutdown multiple apps will crash.

version: kdebase3-3.5.6-42.2
another backtrace:
Using host libthread_db library "/lib/libthread_db.so.1".
[Thread debugging using libthread_db enabled]
[New Thread -1232611664 (LWP 4188)]
[KCrash handler]
#6  0x6f697461 in ?? ()
#7  0xb6e8c785 in QDesktopWidgetPrivate::~QDesktopWidgetPrivate ()
   from /usr/lib/qt3/lib/libqt-mt.so.3
#8  0xb6e8c825 in QDesktopWidget::~QDesktopWidget ()
   from /usr/lib/qt3/lib/libqt-mt.so.3
#9  0xb6ee33ee in QApplication::~QApplication ()
   from /usr/lib/qt3/lib/libqt-mt.so.3
#10 0xb7533779 in KApplication::~KApplication ()
   from /opt/kde3/lib/libkdecore.so.4
#11 0xb7ee4f94 in kdemain () from /opt/kde3/lib/libkdeinit_konsole.so
#12 0x080484b2 in main ()

  Meanwhile I can offer debug symbols for the backtrace (https://bugzilla.novell.com/show_bug.cgi?id=237741). Nevertheless I am not sure whether it will make sense to post all these backtraces (multiples for each KDE-app) if I can not provide further information.

*** Bug 143628 has been marked as a duplicate of this bug. ***

KDE should find a way to complete a shutdown even if certain applications have crashed on quit. DrKonqui should use a timeout when showing the backtrace of the crashed application. Just imagine the user has to leave in a hurry after having initiated a shutdown. It will be a bad surprise to find the computer still running some days later because DrKonqi requires the user to press OK for every single crash.

I'd rather have some other features:
1) When a shutdown has been ordered all crash dialogs should be auto ignored.
2) I'd like all crashes logged so it's possible to review them later.
3) I'd like a "Never show me this dialog again" checkbox on the crash dialog.
4) I'd really like to be able to shut down applications and KDE without having anything crash:)

konqueror crash on quit: Bug 146278

Concerning 1. the user should be prompted at the next startup that some programs (a.e.m.accurate: which ones) have crashed during the last shutdown. Crashes may cause data loss so that the user needs to be informed.

Concerning 4. it will propably never be possible to write programs which can never crash in any kind of situation unless we have something like an automated program verification. Nevertheles some kinds of crashes may also be preventible by an appropriate sandboxing mechanism (Bug 145671) besides other things like garbage collection.

Now KPdf has produced the same backtrace as Konqueror on quit (Bug 146278):

Überprüfung der Systemkonfiguration beim Start deaktiviert.

Using host libthread_db library "/lib/libthread_db.so.1".
[Thread debugging using libthread_db enabled]
[New Thread -1230686544 (LWP 28557)]
[KCrash handler]
#9  0xb71e17ad in QDesktopWidgetPrivate::~QDesktopWidgetPrivate ()
   from /usr/lib/qt3/lib/libqt-mt.so.3
#10 0xb71e1855 in QDesktopWidget::~QDesktopWidget ()
   from /usr/lib/qt3/lib/libqt-mt.so.3
#11 0xb723842e in QApplication::~QApplication ()
   from /usr/lib/qt3/lib/libqt-mt.so.3
#12 0xb784cd49 in KApplication::~KApplication ()
   from /opt/kde3/lib/libkdecore.so.4
#13 0x0804fe87 in main ()

Now KDVI has byed with exactly the same backtrace:
Überprüfung der Systemkonfiguration beim Start deaktiviert.

Using host libthread_db library "/lib/libthread_db.so.1".
[Thread debugging using libthread_db enabled]
[New Thread -1230866768 (LWP 8871)]
[KCrash handler]
#9  0xb71827b2 in QDesktopWidgetPrivate::~QDesktopWidgetPrivate ()
   from /usr/lib/qt3/lib/libqt-mt.so.3
#10 0xb7182855 in QDesktopWidget::~QDesktopWidget ()
   from /usr/lib/qt3/lib/libqt-mt.so.3
#11 0xb71d942e in QApplication::~QApplication ()
   from /usr/lib/qt3/lib/libqt-mt.so.3
#12 0xb7820d49 in KApplication::~KApplication ()
   from /opt/kde3/lib/libkdecore.so.4
#13 0x08050457 in main () 

*** Bug 146278 has been marked as a duplicate of this bug. ***

We can't do much with these backtraces unless you follow the steps on http://techbase.kde.org/Development/Tutorials/Debugging/How_to_create_useful_crash_reports

Meanwhile I have installed the packages recommended by techbase.kde.org. 
Nevertheless I will not be able to provide a valgrind or gdb backtrace since these errors do occur only after a long working period and only sporadically. To achieve this I would have to run my whole Kde-session under valgrind/gdb which is almost impossible.

> To achieve this I would have to run my whole Kde-session 
> under valgrind/gdb which is almost impossible. 

The author of Valgrind did just that at the last Akademy, but it does require some pretty hefty computing power to get usable results.

Valgrind can produce useful results even for bugs which are sporadic, so it is worth trying it on just Konsole to see if you get any hints of erroneous activity in the output.  Incorrect program activity can usually be picked up by Valgrind even when it doesn't always lead to a crash.

> To achieve this I would have to run my whole Kde-session 
> under valgrind/gdb which is almost impossible. 

The author of Valgrind did just that at the last Akademy, but it does require some pretty hefty computing power to get usable results.

Valgrind can produce useful results even for bugs which are sporadic, so it is worth trying it on just Konsole to see if you get any hints of erroneous activity in the output.  Incorrect program activity can usually be picked up by Valgrind even when it doesn't always lead to a crash.

Same backtrace quitting Konqueror (3.5.7 release 31.1):
Überprüfung der Systemkonfiguration beim Start deaktiviert.

Using host libthread_db library "/lib/libthread_db.so.1".
[Thread debugging using libthread_db enabled]
[New Thread -1231096144 (LWP 2348)]
[KCrash handler]
#9  0xb745f7b2 in QDesktopWidgetPrivate::~QDesktopWidgetPrivate ()
   from /usr/lib/qt3/lib/libqt-mt.so.3
#10 0xb745f855 in QDesktopWidget::~QDesktopWidget ()
   from /usr/lib/qt3/lib/libqt-mt.so.3
#11 0xb74b642e in QApplication::~QApplication ()
   from /usr/lib/qt3/lib/libqt-mt.so.3
#12 0xb7aca449 in KApplication::~KApplication ()
   from /opt/kde3/lib/libkdecore.so.4
#13 0xb6736d45 in kdemain () from /opt/kde3/lib/libkdeinit_konqueror.so
#14 0xb6855534 in kdeinitmain () from /opt/kde3/lib/kde3/konqueror.so
#15 0x0804e2ff in launch ()
#16 0x0804eb8a in handle_launcher_request ()
#17 0x0804ef0f in handle_requests ()
#18 0x0805010c in main ()

Given that it happens in all KDE applications I don't think it is a bug in Konsole.  

If you set up a fresh new user account (running KDE) does this still happen?  

  Yes, the bug should perhaps be assigned to the kde base system or somewhere else.
  It only happens after having worked for quite a while, usually including multiple suspend and resume cycles. It will be hard to reproduce on a fresh account simply because that takes its while until these kind of crashes occur and because there is not much to do on an empty account.

  Wanna mark this as resolved for now. No crashes were reported for at least the last two shutdowns of kdebase3-3.5.9-67.2. I will reopen this bug as soon as I encounter any further shutdown-crash.