Well, I'm not certain what exact update you are taking, so it's hard saying what the issue is.
*However*, when you take an update from Apple and it doesn't work for whatever reason - and the software updates from the updater are notorious for this - instead, get the full .dmg file and save it to your desktop and try that.
Go here, http://www.apple.com/support/snowleopard/ and to the downloads link and find the installer download that your software update is saying you need.
I am trying to update my software...I currently have the 10.6.6 version and need to update. I have utilized the software update and completed the restarting process but have been unsucessful. I realize this may be a bit outdated as I should have done this update some time ago, therefore I have not been able to find it on the links provided. Thanks for the help.
You want to get the OSX 10.6.8 combo update..
This is the biggun' - 1.09 GB so plan on this taking a while..http://support.apple.com/kb/DL1399
(do the big one first..)
and this is the Supplemental.. a measly 10MB.. http://support.apple.com/kb/DL1429
Download both to the desktop and run the combo. Should work just fine, and be patient on the restart, this will optimize your drive as it's such a large install, so it can take a while.