Well, from what I've researched, this appears to be a PHP language bug that occurs on 64 bit servers. This explains why I suddenly started receiving this error after I moved on to a new server. Apparently, the error is with the PHP strtotime() function. From what I read, it appears that the smarty tag <{$smarty.now|date_format:"%Y"}> utilizes data from the strtotime() function, which causes this specific smarty tag to fail on 64 bit machines. I tried out the strtotime() function on my server, and it generates the error. Also, the result changes every time I refresh the page, which is consistent with the behavior in the themes.
They are working out (or have worked out) a fix for PHP 5 on 64 bit servers, but I don't know if they are doing the same for PHP 4 (apparently they haven't thus far). Thus, theme developers should be aware of this possible smarty tag problem, and maybe update their themes or provide some replacement code for people experiencing this date error.
It would be good to hear from some other XOOPS users, to confirm that others are having the same problem as me. This may become more of an issue as more web hosts update to 64 bit servers.
Here is a link to an old discussion about the PHP bug.
Dave