Error 1718 - File 1234.tmp was rejected by digital signature policy.
After a bit of Googling, I came across two posts on Heath Stewart's blog which exactly described my problem and provided a workaround. Here's a quick summary of how to install SP1 for Visual Studio 2005 on Windows Server 2003:
1. If you belong to a domain, leave it and reboot your machine.
2. Open up the Registry Editor (Start > Run > regedt32) and navigate to HKEY_LOCAL_MACHINE > SOFTWARE > Policies > Microsoft > Windows > Safer > CodeIdentifiers.
3. With the CodeIdentifiers folder highlighted in the left content pane, check to see if an entry called PolicyScope exists in the right content pane. If it does not yet exist, right-click the CodeIdentifiers folder in the left content pane and select New > Key > DWORD Value. Rename the new item to PolicyScope.
4. Right-click the PolicyScope key in the right content pane, select Modify and change the value to 1.
5. Open up a command prompt (Start > Run > cmd), type net stop msiserver and press Enter to stop the Windows Installer service.
6. Install Service Pack 1 for Visual Studio .NET 2005.
7. If you had to create the PolicyScope key in Step #3, delete it. If the PolicyScope key was already there when you opened up the registry, change its value to 0, using the steps described in Step #3.
8. If you had to leave a domain in Step #1, rejoin it and reboot your machine.
I'm hoping these type of problems go away by the time Service Pack 2 is ready. But for now, I'm just glad I was able to install SP1 without too much difficulty. Thanks, Heath!