SWO  Assuming that you backup, restore iTunes from your last backup (I personally use Retrospect), and drag it to your Applications folder. If you choose to you can then replace the updated version.

This method worked really well for me when I was putzing around with iTunes and 'broke' it.  
(Version 7.3.1)

KINREAD DESIGN  I have had exactly the same trouble. iTunes won't launch despite uninstalling, reinstalling, deletion of library, removal of other programs, etc. Going to have to revert to previous version, what a waste of time!  
(Version 7.3.1)

MACUPDATE ADMIN  First, does your system meet with the requirements for the Security Update you are trying to install?

If so, then try running all your utilities, maybe start with Apple's Disk Utility and repair permissions, then OnyX or something similar to delete all your caches. Maybe you even need to run DiskWarrior or similar app. Then try again to install the update.  
(Version 2007-002)

ADONSA  Nusentinsaino has a valid point.

I experienced the same error after accomplishing full diagnostics

-- Ran Disk Utility

-- Repaired Permissions

-- Ran Onyx - Every diagnostic Onyx is capable of.

Did all the above on two completely different bootup volumes running System Tiger 10.4.8.

All diagnostics passed.

Neither Apple Computer nor this website explains what the "requirements" are that are not being met.

If the Apple staff would be so kind as to publish a list of the requirements for performance of the security upgrade, then we wouldn't be jerked around like Pee Cee users.

Again, Nusentinsaino's question is valid and has yet to be answered.

Regards.  
(Version 2007-002)

NUSENTINSAINO  Indeed, I did run the repairing and Onyx and it still will not accept the security update. Thanks for the information though.  
(Version 2007-002)