1. Read in a list of files in the directory.
   
2. Loop through the files. For each file:
   
3. -- Read in the file contents.
   
4. -- Loop through the files again (requires a second job, since VC doesn't otherwise support nested loops).
   
5. -- If the file name is different from the current file name in the outer loop (and the file's create date time is greater than that of the outer loop's file), read in the file contents.
   
6. -- Compare the contents of this file with the contents of the file in the outer loop. If they're the same, make note of this file name.
   
7. Once the outer loop has ended, I should have a list of duplicate filenames. Loop through them and delete them.
   

Here's a PowerShell script that we use in some jobs to remove duplicate files. Call the script and pass the following parameters to it:
-FolderPath : the folder to work in.
-Recurse : Whether or not to recurse into subfolders.
-Interactive : Whether or not to let the user review the changes and approve them.
The script first builds a list of files where more than one file is the same size. It then hashes each file in that list so that it's finding files with duplicate content, regardless of the file name or date..

# Removes duplicate files from a folder.
Param(
	[Parameter(Position=0,Mandatory=$true,ValueFromPipeline=$true)][string]$FolderPath,
	[Parameter(Mandatory=$false)][ValidateSet('Y','Yes','N','No')][string]$Recurse = 'No',
	[Parameter(Mandatory=$false)][ValidateSet('Y','Yes','N','No')][string]$Interactive = 'No'
)
if ($FolderPath -match '[\*\?]') {
	Write-Output "Path '$FolderPath' invalid.  Wildcards not allowed."
	exit
}

if ( -not (Test-Path -LiteralPath $FolderPath -PathType Container) ){
	Write-Output "Path '$FolderPath' not found or is not a folder."
	exit
}

if ($Recurse -match '^y$|^yes$') {
	$multipleSameSize = Get-ChildItem -Path $FolderPath -Recurse | Group Length | ? {$_.Count -gt 1} | Select -ExpandProperty Group | Select FullName
}
else {
	$multipleSameSize = Get-ChildItem -Path $FolderPath | Group Length | ? {$_.Count -gt 1} | Select -ExpandProperty Group | Select FullName
}

if ($multipleSameSize.Count -eq 0) {
	Write-Output "No duplicate files found."
	exit
}

$fileHashes = foreach ($i in $multipleSameSize) {Get-FileHash -Path $i.FullName -Algorithm SHA1}

$dupFiles = $fileHashes | Group Hash | ? {$_.Count -gt 1} | % {$_.Group | Sort Path | Select Path -Skip 1} | % {ls $_.Path} | Select FullName,Length,LastWriteTime

if ($dupFiles.Count -eq 0) {
	Write-Output "No duplicate files found."
	exit
}

if ($Interactive -match '^y$|^yes$') {
	$userResponse = $dupFiles | Out-GridView -Title ($dupFiles.Count.ToString() + " files to be deleted. " `
													+ $($dupFiles | Measure-Object -Property Length -Sum).Sum.ToString("#,###") `
													+ " bytes recoverable.") -PassThru
	if ($userResponse.Length -gt 0) {
		Write-Output ("Deleting " + $userResponse.Count.ToString() + " files to recover " + ($userResponse |  Measure-Object -Property Length -Sum).Sum.ToString("#,###") + " bytes.")
		$userResponse | % {Remove-Item -Path $_.FullName}
	}
}
else {
	Write-Output ("Deleting " + $dupFiles.Count.ToString() + " files to recover " + ($dupFiles |  Measure-Object -Property Length -Sum).Sum.ToString("#,###") + " bytes.")
	$dupFiles | % {Remove-Item -Path $_.FullName}
}

Thanks! That looks like a useful script for what I need to do. One thing though, does it delete ALL duplicate files? E.g. if it finds 2 copies of the same file, would it delete both of them, or would it only delete 1 of them and leave the other one?

$dupFiles = $fileHashes | Group Hash | ? {$_.Count -gt 1} | % {$_.Group | Sort Path | Select Path -Skip 1} | % {ls $_.Path} | Select FullName,Length,LastWriteTime