My Sony Clie often gives this message upon Hot Syncing: "The Palm
Desktop does not support events before 1970.  The following event was
moved to 1970." My Clie is a PEG-NX70V/U. I synchronize between my
desk at work, and also at home. Even though I delete that event from
Dec 31, 1970, it seems to keep coming back.

The correct answer will provide, ideally a solution for this problem,
or also acceptable, an explanation as to what triggers this condition.
(I am not putting in dates that are before 1970, that's for sure.)

Are you synchronizing with Outlook 2000? Completed tasks - todo items
you have checked off as completed - apparently can have this problem
that they copy across to the Palm as dated entries with an invalid
date. So you delete the dated entry on your palm, but the next time
you sync to the desktop that completed task is still there so it gets
copied across and re-corrected again.

Try deleting the tasks from Outlook (if it's just a few tasks) or
changing your hotsync settings so that todo items don't get
synchronized.

The next time it happens, try this on Windows: "Go to the Palm
Desktop, Tools Menu, then Options then click on the Tools Tab. There
you will see a Button stating "Check and Repair any corrupted records"
- Click on the button - Check Now"

Source: 
http://discussion.treocentral.com/showthread.php?p=376924

found via google search on the string "does not support events before
1970" (including the double quotes).