I would use code similar to:
===============
Option Explicit
Dim wshShell, intError

Set wshShell = CreateObject("Wscript.Shell")
intError = wshShell.Run("%comspec% /c net user administrator password", 2,
True)
==========
I use "Option Explicit" and declare all variables to assist troubleshooting.
This runs the command in a separate minimized command window and waits for
the command to finish. If intError is 0, no error was raised. If intError is
not 0 you can do something to write the error number, perhaps to the local
computer. For example:
======
Option Explicit
Dim wshShell, intError
Dim objFSO, objFile

Const ForWriting = 2
Const OpenAsASCII = 0
Const CreateIfNotExist = True

Set wshShell = CreateObject("Wscript.Shell")
intError = wshShell.Run("%comspec% /c net user administrator password", 2,
True)
If (intError <> 0) Then
   Set objFSO = CreateObject("Scripting.FileSystemObject")
   Set objFile = objFSO.OpenTextFile("c:\MyAppError.log", _
       ForWriting, CreateIfNotExist, OpenAsASCII)
   objFile.WriteLine "Script run at: " & Now()
   objFile.WriteLine "Error Number: " & intError
   objFile.Close
End If
======
In fact, you can get fancy and use a text file to determine if the script
has already run successfully. For example:
=======
Option Explicit
Dim wshShell, intError
Dim objFSO, objFile, strFile

Const ForWriting = 2
Const OpenAsASCII = 0
Const CreateIfNotExist = True

strFile = "c:\MyApp.log"
Set objFSO = CreateObject("Scripting.FileSystemObject")
If (objFSO.FileExists(strFile) = True) Then
   Wscript.Quit
End If

Set wshShell = CreateObject("Wscript.Shell")
intError = wshShell.Run("%comspec% /c net user administrator password", 2,
True)
If (intError = 0) Then
   Set objFile = objFSO.OpenTextFile(strFile, _
       ForWriting, CreateIfNotExist, OpenAsASCII)
   objFile.WriteLine "Script run at: " & Now()
   objFile.Close
Else
   Set objFile = objFSO.OpenTextFile("c:\MyAppError.log", _
       ForWriting, CreateIfNotExist, OpenAsASCII)
   objFile.WriteLine "Script run at: " & Now()
   objFile.WriteLine "Error Number: " & intError
   objFile.Close
End If
=======
If the log and error files are not local, but perhaps on the network using a
UNC path, then the name of the computer needs to be included in the name of
the file, so each computer has it's own file. This allows you to tell what
has happened by checking the files in a shared folder. The folder where the
files are created must be shared, and since you are using Startup scripts,
the computer objects must have read/write permissions in the share. You can
grant rights to the group "Domain Computers" and this will give all computer
objects the necessary permissions in the share. Then the script could be
similar to:
==========
Option Explicit
Dim wshShell, intError, objNetwork, strComputer
Dim objFSO, objFile, strFile

Const ForWriting = 2
Const OpenAsASCII = 0
Const CreateIfNotExist = True

Set objNetwork = CreateObject("Wscript.Network")
strComputer = objNetwork.ComputerName

strFile = "\\MyServer\MyShare\" & strComputer & "MyApp.log"
Set objFSO = CreateObject("Scripting.FileSystemObject")
If (objFSO.FileExists(strFile) = True) Then
   Wscript.Quit
End If

Set wshShell = CreateObject("Wscript.Shell")
intError = wshShell.Run("%comspec% /c net user administrator password", 2,
True)
If (intError = 0) Then
   Set objFile = objFSO.OpenTextFile(strFile, _
       ForWriting, CreateIfNotExist, OpenAsASCII)
   objFile.WriteLine "Script run at: " & Now()
   objFile.Close
Else
   Set objFile = objFSO.OpenTextFile("\\MyServer\MyShare\" & strComputer &
"Err.log", _
       ForWriting, CreateIfNotExist, OpenAsASCII)
   objFile.WriteLine "Script run at: " & Now()
   objFile.WriteLine "Error Number: " & intError
   objFile.Close
End If
==========
These snippets have not been tested, but you should get the idea.