If you want to check an application installed on a computer or multiple server or client computers remotely, you can use Get-WmiObject remotely.

In this scenario, I want to check any client computer that still installed “Microsoft Office Professional Plus 2010”. Here is the command for a single computer remotely:

Get-WmiObject win32_product -ComputerName computername | where{$_.Name -like "Microsoft Office Professional Plus*"} | select Name,Version

If you want to scan or check on multiple computers. You need to get a list of computers first that need to be scanned. In this scenario, I stored the computer list in a folder on C:\ drive.

$Serverlist = Get-content C:\folder\computerlist.txt

Foreach ($Server in $Serverlist) {
$check = Get-WmiObject win32_product -ComputerName $server
If ($check.Name -like "Microsoft Office Professional Plus 2010") {Write-Host "$Server Installed Office 2010"}
Else {Write-Host "$Server No"}
}

This can be used to check any application installed on the client computers. However, this requires remote powershell, and this only detects any application that showing up on add and remove program on the client.