I just did the software update to 10.3.7 and now experience exceptionally long boot times. What happens is that the background image, and top right menu items come up, but the spinning beach ball sits there.
I'm getting a lot of freezes in Safari (which is using more and more of my CPU every day), and sometimes the cursor on one of my monitors just disappears...
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"I've been known to have a drink to celebrate falling down."--Carolyn Mark
There is hope before Tiger gets here: 10.3.8 is on the way in the next few days or weeks. Presumably Apple is aware of this kind of issue, so there should be a fix in the update.
In general, there's no reason not to sleep instead of shutting down. If security is a concern, turn on Fast User Switching (create a second user account if necessary); when you want to leave the machine, select "Login Window..." from the menu in the upper-right corner of the screen. (This menu only appears when Fast User Switching is active.) You don't log out by doing this; you're still logged-in in the background, so your slow login times shouldn't be a factor.