Occasionally, when moving the cursor using the touchpad, the cursor flies away to an irrelevant place, popping up an irrelevant menu. Thereafter, in order to get the touchpad "button" action to work (either by touchpad tap or button), I need to switch workspaces. Even after that, in order to get it to work in a different rectangle (e.g. a different pane of the mail reader) I need to switch workspaces again.

The computer is Dell Latitude 600.
The touchpad is Alps PS/2 DualPoint. Its device is /dev/input/mice. Its driver (according to hwbrowser) is "synaptics."
The kernel is 2.6.18-164.15.1.
The distro is CentOS release 5.4 (Final).
X is xorg-x11-server-Xorg-1.1.1-48.67.el5_4.1, set up for "click to focus".
KDE is 3.5.4-25.el5.centos.1 Red Hat

There are two input device paragraphs in xorg.conf; I don't know which one pertains to the touchpad:

Section "InputDevice"
Identifier "Mouse0"
Driver "mouse"
Option "Protocol" "IMPS/2"
Option "Device" "/dev/input/mice"
Option "ZAxisMapping" "4 5"
Option "Emulate3Buttons" "yes"
EndSection

Section "InputDevice"
Identifier "Mouse1"
Driver "mouse"
Option "Protocol" "Microsoft"
Option "Device" "/dev/input/mice"
EndSection

Any suggestions what to do to correct the problem?

Simply comment one of those out, they are both handling the same device. This is likely why you are having problems.