shorter/cleaner way of writing this

You've got this about as clean as you can get. One thing, you've got a comma after the 2nd entry in the $VLC_Uninstall array, which will throw an error when you try to make the declaration.

You can do test-path and resolve-path with wildcards.

Does it install like a normal program? Usually you'd check the registry for the uninstall key and then execute the executable listed.

Instead of hard coding the VLC Uninstall paths, you could grab them from the Reg. Sure, this complicates the process a bit, but it means you're only grabbing VLC uninstall paths stored in the reg, which should be valid. Plus, if VLC isn't installed in Program Files, it'll have the correct uninstall path. So no guessing where its installed!

something like:

# Get all Uninstall items from the Reg store as pipeline variable.
Get-ChildItem HKLM:\SOFTWARE\Microsoft\Windows\CurrentVersion\Uninstall -PipelineVariable p | 
# Get each entries properties
Get-ItemProperty | 
# Select the properties
Select-SelectObject @{Name="Path";Expression={$p.name}},Displayname,DisplayVersion,Publisher,InstallDate,InstallLocation,Comments,UninstallString | 
#Filter the list based on items display name.
Where-Object {$_.DisplayName -like "*VLC*"}

You'll get an object back that you can then use in part of your script.

Path            : HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Uninstall\VLC media player
DisplayName     : VLC media player
DisplayVersion  : 2.2.6
Publisher       : VideoLAN
InstallDate     :
InstallLocation : C:\Program Files\VideoLAN\VLC
Comments        :
UninstallString : C:\Program Files\VideoLAN\VLC\uninstall.exe

So your resulting script will look like this:

# Get all Uninstall items from the Reg store as pipeline variable.
$VLC_Uninstall = Get-ChildItem HKLM:\SOFTWARE\Microsoft\Windows\CurrentVersion\Uninstall -PipelineVariable p | 
# Get each entries properties
Get-ItemProperty | 
# Select the properties
Select-object @{Name="Path";Expression={$p.name}},Displayname,DisplayVersion,Publisher,InstallDate,InstallLocation,Comments,UninstallString | 
#Filter the list based on items display name.
Where-Object {$_.DisplayName -like "*VLC*"}

# Loop through the results
foreach($uninstall in $VLC_Uninstall){
    # Test to ensure the path is valid
    if(test-path $uninstall.uninstallstring){
        # Start the uninstall process silently
        Start-Process -FilePath $uninstall.uninstallstring -ArgumentList "/S"
    }
}

This could be adapted to create a cmdlet that lets you uninstall a software based on its displayname (not just VLC).

This approach would cover ALL non-standard installation paths. So if your worried about people who might have installed VLC in to "C:\trying to hid this from the admin so he cant uninstall it on me\vlc" you'll get it ;)

Could always put them in a CSV and import it using Import-Csv

I don't know how scalable you want this to be... honestly, if code works for the task at hand, leave it alone. If you're 110% sure you're going to use it again for a similar function, then re-factor it as a function.

If you want to re-use this for other programs, most programs install under the two directories you mentioned. So you could take the common "C:\Program Files" and "C:\Program Files (x86)" out of the array and define them as a static "installation path" array (which you can add to in future). Then instead of using an array for the programs being uninstalled, you could use a hashtable where the key is the folder it would be in and the value is the product-specific uninstall file.

... But you probably now realize that what I said before holds true :-) Your code works! In the Perl language, we say TMTOWTDI (There's More Than One Way To Do It), which is a principle that means 1+ 3 == 2 + 2, and neither statement is "better".

Alternatively you could use the Get-WMIObject cmdlet to get the win32_product object class, filter that for what you need then call $app.uninstall() and not have to worry about locating where the uninstall.exe is, but either way those will do the same thing.

Only shorter way I can think of is to use foreach-item.

$VLC_Uninstall | foreach-item{ 
    if (test-path $_) 
    then{#stuff}
}

But that's just trimming characters.

$args = '/silent'

'C:\Program Files (x86)\VideoLAN\VLC\uninstall.exe',
'C:\Program Files\VideoLAN\VLC\uninstall.exe' |
  Where-Object {Test-Path $_} |
  ForEach-Object {& $_ $args}

Here is a way to use a switch statement. Not sure if its shorter/cleaner, but another way to look at it.

$Paths = "C:\Program Files (x86)\VideoLAN\VLC\uninstall.exe","C:\Program Files\VideoLAN\VLC\uninstall.exe" | where{(Test-Path $_) -eq $True}
Switch ($Paths){
    "C:\Program Files (x86)\VideoLAN\VLC\uninstall.exe" {Start-Process "C:\Program Files (x86)\VideoLAN\VLC\uninstall.exe" -Wait}
    "C:\Program Files\VideoLAN\VLC\uninstall.exe" {Start-Process "C:\Program Files\VideoLAN\VLC\uninstall.exe" -Wait}
}

A few more lines, but cleaner:

$Path1 = "C:\Program Files (x86)\VideoLAN\VLC\uninstall.exe"
$Path2 = "C:\Program Files\VideoLAN\VLC\uninstall.exe"
$Paths = $Path1,$Path2 | where{(Test-Path $_) -eq $True}
Switch ($Paths){
    $Path1 {Start-Process $Path1 -Wait}
    $Path2 {Start-Process $Path2 -Wait}
}