Since I applied the update last night, my iMac will no longer remain in Sleep Mode. When I set it to Sleep, it wakes itself up about 10 seconds later.

I used the 10.5.7 Combo Updater downloaded from Apple's website, because Software Update was having trouble verifying that the data it was downloading was coming from a reliable Apple source. The update process included one incident, where after applying the update and restarting the computer did not fully boot. I waited 20 minutes through an unchanging blue screen, then did a manual shutdown and startup, after which the update completed installing (the computer rebooted itself twice) and, except for this sleep issue, everything seems fine.