I took my battery-operated clock-radio, which I purchased in Saudi
Arabia to South Africa. Once I got there, it no longer worked; it
wouldn't turn on, it was completely dead. However, when I returned to
Saudi Arabia (The Northern Hemisphere), not only did the clock start
to work again, but it reset itself to the manufacture date & time
(midnight on Jan 1 1996). I wonder if this has to do with
magnatic-field differences between the Southern and Northern
Hemisphere and what kind of other devices or things could be affected
by this, or was my clock just malfunctioning. Thanks.

It's just your clock being wacky. If it works solely off of batteries,
then it was acting strangely.  If it was a battery operated type that
you plug in the wall, then you came up against differences in
operating voltages. There is no discernable difference in magnetic
fields between the N/S hemispheres.

Hope this helps.

Absolutely not, your clock is just fine, if voltage was the case, your
clock would have been burnt and would not work when you got home. All
it is is the frequency in the voltage cycle, in North america the 60HZ
cycle is observed and in other part of the world even though the
voltage maybe the same, the frequency used is most of the time lower
ie: 50HZ or very few places higher.
A very good example is in airplanes, the groomers use a regular 120V
vacuum cleaner, however, that vacuum uses 100HZ cycle so if you plug
in any electrical devices it will not work, actually it might do
damage to it due to higher frequency that is being used.
Hope this clarifies things.