For some insane reason, Windows XP SP 3 won't install if you have a certain hotfix/patch installed. There's no way to uninstall it, but I found this workaround - which worked fine:
When installing today Windows XP SP3 from Microsoft Update, I got an error message immediately after it began downloading the update. Tried downloading the entire package from the Microsoft Download Center and after unpacking the installer, I got an error message saying that I needed to uninstall KB925877, a package related to remote desktop connection.
If you have installed the latest version of RDP, then you must have installed the package KB925877, but this package is not visible on the Add/remove programs, so you can't uninstall it on that location, you must search on the registry editor and delete the corresponding registry.
The exact path is HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\Current Version\Hotfix\KB925877.
Just delete the registry and try installing SP3 one more time, it should run fine and won't give you any other error messages.