If it hasn't already, your Software Update will soon offer you to update to OS X 10.3.9. You can go ahead and do this.
The only possible glitch I have heard of is Java apps misbehaving in Safari, or Safari failing to launch. If you observe any weirdness in Safari, re-install the "2005-002" security update. It is available at 3 Resources : Mac OS Files : SecUpd2005-002Pan.pkg. Apple has a page on the issue.
Incidentally, this is likely the last update to Panther before OS X 10.4 ("Tiger") is released at the end of the month. That is a major update and we will handle it as wait-and-see.